BACKGROUND

In this article we are aiming to build cognitive semantics over a first person perspective. Our goal is to specify meanings connected to cognitive agents, rooted in their experience and separable from language, covering a wide spectrum of cognitions ranging from living organisms (animals, pre-verbal children and adult humans) to artificial agents and that the cognitive semantics covers a broad, continuous, spectrum of meanings. As regards the used method, the first person perspective enables a kind of grounding of meanings in cognitions. An ability of cognitive agents to distinguish is a starting point of our approach, distinguishing criteria and schemata are the basic semantic constructs. The resulting construction is based on a projection of the environment into a cluster of current percepts and function on percepts. Situation schemata, more sophisticated similarity functions, event schemata and distinguishing criteria are built over that basis. Inference rules and action rules are components of our semantics. An interesting property of the proposed semantics is that it makes possible coexistence of subjective and intersubjective meanings. Subjective (first person perspective) meanings are primary, and we have shown the way from them to collectively accepted (third person perspective) meanings via observable behaviour and feedback about success/failure of actions. An abductive reasoning is an important tool on that way. A construct of an instrument, which represents a measure for using intersubjective meanings, is introduced. The instrument serves as a tool for an inclusion of sophisticated meanings, e.g. of scientific constructs, into our framework.


INTRODUCTION BACKGROUND
This article focuses on meanings.Traditional semantic theories almost exclusively dealt with meanings of linguistic expressions.Elements of language were either mapped to sets of objects and relations in the world (in extensional semantics, e.g.[1]) or to mappings from possible worlds to sets of objects and relations (in intensional semantics, e.g.[2,3]).In any case, meanings were seen as something objectively existing regardless of any interpreting subjects.This so called objectivist approach has been criticized by Lakoff [4] 1 who proposed an alternative called experientialist approach.Within this approach, meanings are rooted in experience of physically embodied 2 beings, and this experience is richly structured even before language and independently of it.Lakoff's book has started an entirely new research program called cognitive semantics that no longer places meanings in the outside world.Meanings are mental entities and are conceptualized by image schemas and idealized cognitive models [4], geometrical or topological structures in so called conceptual space [5], or force dynamics patterns [10].Relation of meanings to language, especially grammar, has been further elaborated e.g. in [11][12][13][14].
Cognitive semantics in its various forms has been around for about 25 years; still it has not given a satisfactory account of many issues.It has been criticized for absence of a satisfactory account of semantics of verbs and sentences/propositions and no theoretical account of how the proposed conceptual structures can be constructed; the proposed structures were intuitively plausible only for a small subset of basic cases and solutions for more complex cases were often described vaguely and in an ad-hoc manner [15, chap. 2].In the next two sections we will specify problems that we try to address in this article and a quick view on their proposed solution.After that, more thorough motivation is given.

PROBLEM
Although cognitive semantics theoretically claims that meanings are "in the heads" of cognitive agents, they are almost exclusively studied and defined as if viewed from outside by an independent observer (from the third person perspective).Definitions used presuppose a common understanding of terms, which is often taken for granted.Also, it is quite modern to literally "look into the head" and search for neural correlates of meanings, e.g.[16,17].While we believe that such approach is certainly useful, in this article we want to forget about the brain and take more phenomenological stance.An open problem is to ground meanings by the first person perspective and subsequently to build an integrated theory of meaning over that basis.
This basic problem generates a series of other problems.We find as interesting to describe how it is possible to integrate purely subjective meanings with intersubjective meanings, meanings accepted by a society, meanings assigned to abstractions created in terms of a language and/or corresponding in a way to an external environment (and how those meanings may coexist).

PROPOSED SOLUTION
We propose a solution based on an ability of cognitive agents (and more generally, an ability of living organisms and their parts) to distinguish.This ability is demonstrated also as a selection/construction of a schematic view on a complex chunk of percepts (or more abstract entities).Our basic semantic constructs are schemata and distinguishing criteria, abstractions of the ability to distinguish.A background idea behind is an assumption that some meanings may be independent of (or even prior to) a language.
Similarly, we view and construct the world of meanings as a continuous one, containing a broad spectrum of meanings, from those which can be ascribed to animals or preverbal infants on one side to meanings, assigned to a language with a rich syntactic structure on the other hand.This approach to cognitive semantics was first proposed in [18].Distinguishing criteria conceived as functions were defined as abstraction of the ability to distinguish.Basic types of criteria of objects, classes, properties, relations, situations, changes, and plans were proposed, together with the way from pre-verbal biological roots through semantics of two-word language to language with full syntax and reasoning.The theory was further enhanced with more elaborated situation criteria [19] and short term (focus, situation, problem, event) and long-term (situation/event types, situation/action rules) distinguishing criteria [20].The paper [20] also analysed a case study of animal behaviour [21] in terms of the semantics of distinguishing criteria.In [22] we described a computational implementation of the framework focusing on autonomous construction of distinguishing criteria in interactions with the environment.In [23] we further elaborated the semantics of events and implemented it in a computational model.
The semantic framework of distinguishing criteria has been being developed for ten years.So far we and our students have produced 28 papers, eight master theses and one dissertation thesis elaborating various aspects of the theory and simulating its partial computational models.However, much of our work has only been published in Slovak yet, hence inaccessible to the wider audience.This article intends to be comprehensive, but the theory presented here is substantially refined and different from our previous work.We will return to their comparison in Conclusions.

MOTIVATION
Let us motivate the first person perspective on meanings in more detail.A paradigmatic stance of science towards objects of research is to remove all marks of subjective points of view, to be looking on those objects as independent of the opinion of a researcher.Objects of a scientific research can be viewed metaphorically as the third persons.Also meanings, according to that attitude, are usually objects of research, independent of a researcherthey should be viewed as "It".
Our approach to cognitive semantics is based on another stance: we start from subjective meanings (meanings adopted by an animal, by a preverbal infant, by me etc.).Hence, we start from the first person perspective and on that basis we try to reconstruct intersubjective meaningsmeanings common to more agents and also meanings which may be understood as objective entities, metaphorically located in the realm of ideas.
We believe that such construction could be fruitful for cognitive semantics: the first person perspective enables a kind of grounding (embodiment) of meanings in cognitions of agents and the reconstruction of intersubjective meanings on the basis of subjective meanings completes the picture.Actually, there are many roles of meanings, from understanding of a local environment of an agent to mutual communication of ideas in a society or to an exactly verified view on the world.Now a more detailed motivation for our basic semantic constructs follows.Our goal is to propose a semantic framework joining (integrating) all meanings, from purely subjective ones to intersubjective meanings, supported by a somehow codified status.
The central building blocks of the frameworksemantic constructs called distinguishing criteria and schemata, cover a broad spectrum of meaningsfrom meanings which can help us to explain behaviour of animals to semantics of languages with rich syntactic structure.
The framework enables coexistence of subjective and intersubjective meanings, understanding of different, but mutually close, subjective meanings and a characterization of a development of intersubjective meanings on the basis of subjective meanings.This ambition is based on a belief that there are no strict boundaries between living organisms and capabilities of living organisms evolved continuously in the nature.There is also a continuum of cognitive capabilities in the nature; those capabilities are implemented through cognitive processes, their results can be considered as meanings and, finally and consequently, the world of meanings is continuous, without strict boundaries.This world is inhabited by subjective meanings of cognitive agents on initial stages of their mental development (imagine a little child which denotes also pigeons by the word "dog"), by meanings evolved from those initial ones, by meanings of expressions of languages with different levels of complexity, by meanings acquired in times of the elementary school etc.New strata of meanings are placed permanently over the previous ones.This continuous world of meanings reaches up to meanings of scientific theories.
Meanings assigned to animal cognition deserve an additional explanation.The analysis of animal behaviour leads to conclusions that animals are able to reason and that they have knowledge about the external world [20].They observe results of their own actions or of actions of other agents.They distinguish success or failure of actions and learn on the basis of such observations.It can be said that they understand relevant features of the environment.This understanding can be described in terms of meanings.
Even a stronger and more general claim is justifiable.We do not assume that meanings are assigned only to language expressions.To the contrary, meanings are prior, in a sense, to language expressions.An acquisition (and also a development) of a language is possible only if some meanings are sooner acquired by the future users of the language.A little child is able to use a word correctly, to acquire a meaning of a word only after it is able to recognize, to distinguish the corresponding referent or situation in the environment. 3Similarly, animals are able to recognize, to distinguish some important objects, their properties, situations in the environment without a use of a (human-like natural) language [21].As a consequence, we believe that an understanding of a stratum of some language expressions is possible only on the basis of some experience with meanings of some more elementary strata of the language.This also holds for understanding of abstract expressions.In that case an experience with abstract objects is required, e.g.we can understand the notion of the (mathematical) derivative only after some (computational and conceptual) experience with the notion of the limit of a function.

BASIC FEATURES OF OUR SEMANTICS
We emphasize cognitive nature of meanings.Objects of the real world, their properties, classes of objects etc. are traditionally considered as meanings.Meanings in our semantics are embodied in a sensethey are connected to cognitions (cognitive agents 4 ), and they are our abstractions of capabilities of cognitive agents.Two important points should be explained in the context of the previous sentence.Meanings are constructed by cognitive agents (i.e., our position is constructivist [25]): if an agent distinguishes something and a meaning is identified with the ability to distinguish, then the meaning is a product of the agent.On the other handmeanings are not reducible to mental or neural processes.Cognitions are connected to the external environment.Contents of cognitions are dependent on the state of the external world (this can be denoted as an externalist position).However, when we speak about this relation between cognitive agents and the external world, we locate meanings on the side of the agents.We are not interested in meanings which could exist without agents.This is the reason why our semantics could be considered as cognitive semantics.
In this article, we are not going to enter debates about true ontological status of meanings; rather we conceptualize them by constructs which enable to explain some observable features of the behaviour of cognitive agents.
We sum up and motivate some important properties of our semantics.A satisfaction of those properties is important, if we want to build a realistic account of meanings used by cognitive agents.
1) First, we emphasize an evolutive nature of meanings.The experience of cognitive agents leads to some updates or revisions of their beliefs and notions.Notice that beliefs are in our approach meanings -we do not identify beliefs of agents with a knowledge base in a form of sentences of a language, but we view them as a cluster of meanings.Also extensions of knowledge bases and of the conceptual apparatus of an agent should be considered as an evolution of meanings because of mutual dependencies of pieces of beliefs and of concepts.2) Further, an approximate nature of meanings should be taken into account.Meanings (most importantly, beliefs and also meanings of sentences) are constructions of the agents.Our opinion is that those constructions could be, and often are, improved, précised.The evolutive and approximate natures of meanings are two sides of the same coin.The second one stresses impreciseness of meanings, the first one their development in time, which may sometimes lead to more precise meanings.3) Fluent nature of meanings is something different from both features mentioned above.
The world of meanings contains many examples of similar meanings with small continuous differences.4) Usually, meanings are treated as independent of knowledge.It is argued that knowledge is composed of words and their meaning is given.We believe that meanings are tightly connected to knowledge.Recall our opinion that knowledge bases of cognitive agents are constructed of meanings, not of words.When a knowledge base is built, a set of meanings is built.What is important, meanings of words are acquired, modified, made more precise in the context of the knowledge base.If we want to express something more subtle, words are selected in a stepwise way, their meaning is fluently changed and accommodated in order to reach a satisfiable final or preliminary expression of our evolving idea.5) Similarly, meanings are tightly connected to reasoning.Cognitive agents need to reason, in order to understand and create meanings.6) Some meanings are dependent on context, viewpoint and temporary focus of a cognitive agent.To sum up, we are aiming to build the semantics with evolving, approximate and fluent meanings, which are connected to knowledge and reasoning and dependent on a context.

OVERVIEW
The rest of our paper is structured as follows.First, an analysis of intuitions and different connotations of the word distinguish and its semantic relatives discriminate, identify, recognize is presented.After that, basic ideas and constructs of our semantics are described, explained and defined.We start with a conception of a situated agent ("Me") in an environment.A projection of the environment into a cluster of current percepts and a similarity function on percepts are introduced.Subsequently, situation schemata, representations of percepts, are described together with further important notionsmore sophisticated similarity functions, knowledge base, event schemata and distinguishing criterion of change.A current state of "Me" is defined as a six-tuple comprising of its knowledge base, percepts, beliefs, desires, intentions and behaviour in a given time point.The last one is observable from outside; the others can be seen from the first person perspective only.After that, we introduce transformersdistinguishing criteria that express transformations of schemata.Special types of transformers, called constructors, construct detectorsa type of distinguishing criteria which represent common characteristics of categories recognized on schemata by "Me".Another type of transformersupdaters keep track of evolving schemas and distinguishing criteria.Note that with the developing semantic apparatus, further kinds of similarity functions are introduced.We introduce several types of detectors (of individuals, properties etc.).Inference rules and action rules are built over this equipment.
The subsequent part of the paper describes a way from subjective meanings (of "Me") to intersubjective meanings.That part starts with a look on an evaluation of subjective meanings with respect to observations of success or failure of actions.After that, the third person perspective (of an agent "It") is described.Only actions -the behaviour of "It", are observable.Meanings accepted and used by "It", its knowledge base with beliefs, desires and intentions can be hypothetically derived by abduction.A construct of an instrument, which represents a measure for using intersubjective meanings, is introduced.The measure is accepted by a group of agents, it is generally accessible and interpreted in a unique way.A summary of semantic constructs is presented in Appendix A. Conclusions contain a description of main contributions of this paper and a list of open problems and topics for the future research.

DISTINGUISHING
We consider distinguishing a basic cognitive ability of living systems, ranging from primitive forms such as moving toward/from light or following a gradient of concentration of particular chemicals, to distinguishing members of a category from non-members or judging appropriateness of certain behaviour or a linguistic expression in particular social context.Because of this basic ability, some authors postulate elementary cognition on very low evolutionary levels, such as molecules or simple bacteria [26,27].Before making distinguishing a core element of our cognitive semantics, we would like to analyse different connotations of the word distinguish and its semantic relatives discriminate, identify, recognize.
According to the Oxford Dictionaries, 5 distinguish is a verb meaning to: 1) recognize or treat (someone or something) as different (distinguishing reality from fantasy); recognize or point out a difference (distinguish between two kinds of holiday); be an identifying characteristic or mark of (what distinguishes sport from games?), 2) manage to discern something barely perceptible (it was too dark to distinguish anything more than their vague shapes), 3) (distinguish oneself) make oneself worthy of respect by one's behaviour or achievements (many distinguished themselves in the fight against Hitler).
While the third sense is unrelated to our analysis, the first two senses refer to recognizing/discerning differences, as well as identifying common characteristics.In the same Oxford Dictionaries, the relevant sense of the word discriminate is to "recognize a distinction, differentiate (discriminate between different facial expressions); perceive or constitute the difference in or between (features that discriminate this species from other gastropods)".
Definition of relevant senses of recognize includes "identify (someone or something) from having encountered them before; know again (I recognized her when her wig fell off); identify from knowledge of appearance or character (Pat is very good at recognizing wild flowers); (of a computer or other machine) automatically identify and respond correctly to (a sound, printed character, etc.)".
Definition of identify includes the sense "establish or indicate who or what (someone or something) is (the men identified themselves as federal police); recognize or distinguish, especially something considered worthy of attention (a system that ensures that the pupil's real needs are identified).
The dictionary definitions are somewhat circular, as the meanings of the words identify, discriminate, distinguish and recognize are intertwined; however in the following text we will use the word recognize when emphasizing knowing again, the word discriminate when emphasizing telling a difference, the word identify to establish an identity or a category membership or a state of affairs, a fact, a rule, and the word distinguish in a more general sense encompassing all the previous ones.A similar distinction is made in Harnad's seminal paper [28] in a more technical description of processes in a cognitive system: "To be able to discriminate is to be able to judge whether two inputs are the same or different, and, if different, how different they are.Discrimination is a relative judgment, based on our capacity to tell things apart and discern their degree of similarity.To be able to identify is to be able to assign a unique (usually arbitrary) responsea "name"to a class of inputs, treating them all as equivalent or invariant in some respect.Identification is an absolute judgment, based on our capacity to tell whether or not a given input is a member of a particular category." According to Harnad, discrimination needs so called iconic representations (internal analogue projections on distal objects on our sensory surfaces), while identification needs categorical representations (selected invariant features of icons that reliably distinguish a member of a category from non-members).One of us analysed the difference between discrimination and identification in the context of our semantic theory in [22].
In a sense, the ability to identify (e.g. a particular horse as a horse) presupposes the ability to discriminate (tell apart (at least some) horses from non-horses) and also includes recognition (I could hardly identify a horse if I hadn't seen any horses before).
As our ambition is to build a semantic theory, we cannot avoid the term understand too.In line with our proclaimed goal, we would be willing to extend its meaning beyond the most usual "understand a word or a linguistic expression" toward understanding situations, events, and the world around us.Moreover our notion of understanding or meanings should also include animals, preverbal infants, and even artificial agents.In a basic sense, understanding a situation means reacting to it appropriately with respect to one's goals [25].However, this somewhat behaviouristic definition doesn't include a case when someone understands something without displaying any overt behaviour.Our ultimate definition of (high-level) understanding is "knowing the truth about something and being able to explain why". 6 Elaborating the concept of truth and intersubjective instruments of knowing within the framework of the proposed semantic theory is one of the novel contributions of this paper.

THE FIRST-PERSON SEMANTICS OF "ME"
The goal of this section is to gradually build semantic constructs as they are seen by the cognitive agent itself.However, on the (meta-) level of presentation, we cannot completely avoid the third-person-type descriptions, as we are hoping to transfer our ideas to the reader in interpersonal communication by words with commonly established meaning.The way from subjective to interpersonally accepted meanings is proposed later in the article.

SITUATED AGENT AND ITS ENVIRONMENT
We already mentioned that our semantic framework is cognitive, i.e. we place the meanings inside the cognitive agents.It also significantly overlaps with pragmatics, in the sense that meanings are related to knowledge, understanding and reasoning of a particular agent.Usefulness/correctness of meanings can be tested by pragmatic criteria in the real world/environment (external to the agent).
Imagine a cognitive agent situated in an environment Env.The agent is coupled with its environment via sensing and acting.The environment is dynamic in the sense it can change from moment to moment based on the agent's actions and other factors (external to the agent) including actions of other agents.We will denote a current state of the environment Env t (where t stands for a time point).
Currently being performed actions of the agent constitute its observable behaviour Beh t . 7We assume that the agent has an internal view on itselfits internal state, memories, knowledge, which are not directly observable from outside. 8This view (called "Me") is described in more detail in the following section.The agent is dynamic too, as its internal state and knowledge are changing in time (shaped by its experience).

PERCEPTS
In any moment, the agent's perception of the environment is mediated via its senses.So, the agent views the environmental state as a collection/cluster of current percepts P(Env t ).In this sense, P is a projection function (projecting the environment into the agent's internal perspective) but also a selection function: what exactly is projected is determined by the agent's embodiment and physical limits, 9 its past experiences, its current mental state and focus of attention, etc.
However, we do not ascribe to P much of a sense-making; this is applied to P(Env t ) afterwards.P(Env t ) contains rather crude (low-level) percepts forming iconic representations in Harnad's sense [28] (see section Distinguishing).Iconic representations allow for discrimination, i.e. being able to tell if the things are different/similar, and possibly how different/similar they are.We formalize this subjective discrimination ability by a similarity function sim d .In the first approximation, sim d operates on percepts and is able to detect perceptual similarities/differences; later we extend the agent with more sophisticated similarity functions.

SITUATION SCHEMATA
The similarity function enables the agent to recognize common patterns among recurring percepts and gradually extract schematic views of their relations.In people (and probably other embodied agents too), basic schemata 10 arise directly from recurring sensorimotor experience early in development 11 [31] and more complex ones are gradually built on top of these.Cohen et al. [32] describe how different levels of schemata (perceptual redescriptions) can be learned based on detecting statistical contingences among perceptual streams (e.g.inferring a concept of an object as time-locked correlations of percepts in different sensory streamsa sort of a multimodal integration; see also [33]).Schemata allow the agent to make sense of its current perceptions by establishing their relation to previous experiences (by recognizing similarity and evoking memories) and, more generally, integrate the new experience within the web of existing knowledge (expressed by schemata).This corresponds to Piagetian process of assimilation [31].
In this sense, a sense making act σ (signification [34]) of the agent is a process of constructing or evoking appropriate schemata, given the current percepts P(Env t ).We will denote the result of signification σ(P(Env t )) and call it situation schema.Unlike percepts that are pure transductions of the external environment, a situation schema is a representation with the added value of interpretation of percepts [35].A situation schema can be formally represented by a labelled graph with percepts in vertices linked by edges expressing their mutual relations.More precisely, only some vertices correspond to percepts; other express inferred constructs.For example, if the agent recognizes percepts in multiple modalities as constituting a single object, the graph will contain a separate vertex for this object, with all its percepts linked to it by edges of an appropriate type.The type/semantics of an edge is represented by its label.The object vertex can further be linked to other schemata in memory, recognized/evoked as similar or related in some aspect to this object (e.g.recognizing this object as my dog).Sometimes a relation is so complex it is best expressed by a schema of its own; in that case, a (n-ary) relation is represented by a (n+1-ary) hyperedge 12 with one vertex serving as a handle/access point to another schema.So we can see that the schema can contain vertices of various types.The type of a vertex is expressed by its label.We allow multiple labels for vertices and edges; these can be interpreted as different views on the same situation.Formally we can organize labels in layers (thus creating a layered graph) or we can see the layers as separate schemata linked together (by establishing similarity/identity relations among the corresponding vertices and edges).Later we will define means for transformations among schemata.
In order to establish a relation to previous experiences, the agent needs to maintain some sort of memory.We will call the agent's long term memory its knowledge base KB t .The knowledge base is a set that includes the agent's remembered situation schemata -a subset 13  of { σ(P(Env i )) | i < t } (we will gradually extend the definition of KB t with other constructs).
The knowledge base also contains a set of similarity functions (without going to details, we assume that the agent gradually learns to use functions for detecting similarities/differences among schemata, derived from the most elementary sim d that operates on percepts).

EVENT SCHEMATA
The world around the agent is dynamic; situations change to other situations.A change of one situation to another constitutes an event.Being endowed with similarity functions, the agent is able to perceive temporal changes in situations.We describe this ability by a construct of a distinguishing criterion of change.We formalize a distinguishing criterion of change as a function defined on pairs of the form (σ(P(Env t-1 )), σ(P(Env t ))); if the second one is a result of a change of the first, the assigned value is 1.
The agent represents distinguished events by event schemata.An event schema consist of two or more situation schemata linked by (hyper)edges labelled by distinguishing criteria of change.Event schemata can be constructed or evoked from memory (in case of recognition of a similarity to a past event).We will denote the act of event selection ε and its resulting event schema ε(σ(P(Env t )), KB t ).We will also extend the definition of the knowledge base to include event schemata

CURRENT STATE OF "ME"
So far, the agent's current knowledge base is described as a bag of interlinked schemata of situations and events.However, schemata do not have a uniform status at each moment: some of them describe the interpretation of the current/recent situation/event; others are related or associated to it, yet others are "inactive" at the moment.Some are attended to or focused on, others are not.Moreover, the agent can be in the middle of executing a plan or pursuing a goal.A goal of an agent can be expressed as a situation schema of a desired situation.A problem or a question can be expressed as a situation schema (perhaps with special vertex/edge labels) too.The agent needs to distinguish what a particular schema represents in a momentits particular autoreflexive attitude toward the schema.In the first approximation, we imagine the autoreflexive attitudes are represented by special labels on (elements of) schemata.Current autoreflexive attitudes temporarily give some of the schemata in the knowledge base a special status.These schemata can be further factorized to a current set of the agent's beliefs B t (schemata of currently perceived situation/event), a set of desires D t (schemata of the agent's needs and long-term goals), a set of intentions I t (schemata of the agent's current goal, a plan to achieve this goal together with a state of its execution, and other agenda-related structures). 14A current state of "Me" can be defined as where only the agent's overt behaviour Beh t is observable from outside; all other structures can only be seen from the first person perspective.

TRANSFORMERS
We have said that situations and events are related in various ways.Initially (while the agent's similarity function does not go much beyond crude holistic "same/different" perceptual similarity judgements), the agent's knowledge base will mostly contain holistic "snapshots" of its experiences (schemata with a few basic labels).Later, when the agent has accumulated sufficient number of exemplars, it can extract their common/invariant features, etc. 15 , which results in more complex similarity functions and a richer repertoire of labels.Simpler schemata can be refinedtransformed to more informed ones by adding new layers of labels, simplified (zoomed out) by removing labels, linked to other schemata by associations, pruned by attention shift or focusing on a particular detail (zoomed in), merged (abstraction), etc. [20].
We will formally describe the agent's ability to distinguish (and perform) these (and other) transformations on schemata with a construct of transformer.A transformer is a type of distinguishing criterion that expresses transformations of schemata: it has both a declarative aspect (as a description of relations among schemata) and a procedural aspect (as a device that transforms a schema into another schema).
A special type of transformer is called updater.The concept of updater expresses the idea of evolutive nature of meanings: If some of the agent's meanings change in time, the agent can keep track of this change by using an updater that will take the schema of the old (original) meaning and connect it to the schema of the new (updated) meaning by a specially labelled edge.The same holds for updates of distinguishing criteria.A schema with a single node labelled by an original distinguishing criterion is linked by a specially labelled edge to another schema with a single node labelled by the new (updated) distinguishing criterion.This mechanism helps to preserve the identity of (evolving) meanings.

DETECTORS
By noticing recurring patterns and similarities, the agent can start grouping together situation and event schemata recognized as similar in some respect (i.e. by some similarity function).These groups of similar exemplars constitute elementary types of situations/events.Extracting common features of the exemplars can in turn lead to construction of more sophisticated similarity functions which can be used to factor schemata into categories. 16Special transformers called constructors operate on sets of schemata (exemplars) and construct a new distinguishing criterion representing their common characteristics, called detector. 17 Internally, a detector consists of a schema specifying a template with features important for category membership (in some cases more or less abstract representation of a prototypical, salient or most frequent category member) and a similarity function specifying how important the particular features are and how they contribute to the overall similarity.Functionally, a detector can be formalized as a partial 18 function that operates on (fragments of) schemata and returns their degree of membership in the implicitly represented category (either as 0=no, 1=yes, or by a fuzzy value from the closed interval [0,1]).
A detector operates on schemata (or their elementsvertices and edges) and is able to distinguish not only its constituting exemplars, but also generalize to other similar schemata.Some detectors distinguish situation types (e.g. a traffic jam) and event types (e.g. a car crash), others distinguish their elementsobjects/individuals (such as Barack Obama), classes of objects (dog, stone, food), properties of objects (red, big, hairy), relations between/among objects (bigger than, ancestor), changes (grow, faint).

INFERENCE AND ACTION RULES
Having defined schemata, transformers and detectors, we can revisit the signification and view it as an iterative process; for example the situation schema of a woman with a dog can initially consist of two unidentified objects (linked with their percepts), perhaps linked together by an unlabelled edge.Fragments of this situation schema will then be recognized by detectors vaguely distinguishing dogs and women.Hence, the object vertices will be appropriately labelled by or linked to the detectors.Another detector can recognize their spatial configuration, so the edge connecting the objects will be given a new label too.
This can in turn trigger further transformations on the situation schema, depending on the current context (the current state of "me").The agent can keep track of sequences of transformations typically occurring in certain situations and extract this knowledge in the form of rulesschemata connecting premises (prerequisites -the rule's applicability conditions represented by distinguishing criteria of situation and event types) to consequences (represented either directly by situation and event schemata or indirectly by transformers that can be applied to the current situation/event and construct the resulting one), optionally with justifications (situation and event types guarding the evidence that would prevent the application of the rule in case of default rules; see [20] for more details).Some rules specify dynamics of internal transformations (so called inference rules), others specify the effects of overt actions on the environment (so called action rules, see the next section).Rules can be chained together in the form of plans, presumably leading to satisfaction of a goal.The agent can keep track of success/failure of a plan in the past.Remembered successful plans are called routines.

TOWARDS INTERSUBJECTIVE MEANINGS MEANING AND BEHAVIOUR
A first important step on the way from purely subjective meanings to intersubjective meanings is described in the following paragraphs.
Assume that a cognitive agent ("Me") equipped with subjective meanings only observes results of its own actions or of actions of other agents."Me" distinguishes success or failure of actions and learns on the basis of such observations."Me" evaluates its own behaviour and gets a kind of distinguishing of something what can be regarded as truth.
We will describe how such observations lead to objective meanings, more precisely, how some subjective meanings induce behaviour and how "Me" can assign truth to some schemata.
It was stated in the previous section that some transformers trigger overt behaviour.Actions are represented by complex schemataaction rules.Their consequences are transformers which assign a schema representing a resulting situation to the current situation schema.
Those transformers may have for some agents a rather complex structure.They may realize a short-term mental operationan imagination of the action, a specification or a recall of the required effects of the action and, finally, firing the action.The change specified by the transformer is an expected result of the action and it is expected that the result complies with the specified effects of the action.
Let us describe in more detail how an action rule is selected, fired and how its result is evaluated."Me" non-deterministically selects some desires (represented in its knowledge base by a distinguishing criterion or a schema), transforms them using some transformers onto intentions and subsequently other transformers are used in order to map intentions onto actions (members of Beh).
However, triggering (an attempt to do) an action is essentially a complex trial and error procedure, which comprises learning of prerequisites and effects of the action (operations on situation schemata) and evaluating success/failure of the action.We will describe it in terms of our semantics.
Assume an agent that connects an action rule with a distinguishing criterion of a required change (a goal, a required effect of the action).If the corresponding action was executed, then the premise and consequence of the corresponding action rule may be modified according to the current situation schema and the current change of the situation schema by the action.
If an action should have been executable in a situation (according to the premise of the corresponding action rule), but the attempt to execute it failed, then the agent modifies the premise of the corresponding action rule.There is a variety of possibilities how to modify it [39], but we will not discuss them here.
What is important here, an evaluation of an action rule is based on a comparison of situations (the premise of the rule vs. the situation in which the action was executed; the consequence of the rule and the required effect vs. the real effect of the executed action).
The comparison is described in our semantics in terms of a similarity function.An application of this function, even if it is a subjective distinguishing criterion, enables to evaluate (subjective) meanings with respect to the results of a behaviour in the external environment and to reach a kind of understanding and of an (approximate) truth (or falsity) of prerequisites, effects and action rules, which is dependent on the external environment via the success or failure of observations.
Reasoning capabilities (some transformers, some rules) can be tuned in a similar manner.
A final remarkbesides rules of the structure described above, other complex schemata, such as modalities, deontic constructions, more complex generalizations, etc., are also construable on the basis of situation or event schemata.However, we will not discuss them.As regards the truth or falsity point of view, some actions can serve as tests of their (approximate) truth.
We believe that an evaluation of a success or a failure of actions in an environment enables a stepwise more precise comparison of subjective meanings and a more precise approximation of truth.
Now, when we are equipped with a notion of an approximate truth, we can proceed to a kind of the third person perspective.

THE THIRD-PERSON PERSPECTIVE
The third-person agent, observable from the viewpoint of "Me" may be represented on the basis of pure observations as Ag t = (Beh t ).We canand will -use "It" instead of "Ag".
"Me" considers actions of other agents as events.Suppose that "Me" observes an action of an "It".The current situation and the effect of the action are observable by "Me".On that basis an abduction of action rules of "It" is possible.Similarly for an inference of its P(Env), B, D, I, i.e., KB, by "Me".Notice that the results of this inference are not in general identical to subjective meanings of the agent "It" (to emphasize this difference, we mark the inferred structures with the apostrophe (').We will call them an external view on subjective meanings.
Thus, we can specify a derivable third-person agent: also indexed by the agent if needed.
In general, an external view on distinguishing criteria and schemata of other agents may be specified in terms of distinguishing criteria and schemata of "Me".We can say that "Me" creates a "theory of mind" of other agents.
Some similarity functions enable to identify similarity of subjective meanings of one agent in two different time-points, of distinguishing criteria corresponding to different sensual inputs etc.Most importantly, they enable to compare Me's external views on subjective meanings of two different (third-person) agents."Me" can also compare its own subjective meanings and its external view on subjective meanings of other agents.
Thus, a relation of a close neighbourhood (or of an approximate identity) of two distinguishing criteria or schemata is created for high values of a similarity function.The approximate identity specifies a chunk of distinguishing criteria or schemata and enables a step from subjective to intersubjective meanings.

OTHER STEPS TOWARDS INTERSUBJECTIVE MEANINGS
In this section a brief survey of some possible conditions leading to intersubjective meanings is given.
Similarity functions and their impact on creating close neighbourhood relations represent our attempt to include autoreflexive reasoning into our semantic constructions.Autoreflexive attitudes were discussed in Section Current state of "Me".It was noticed that the simpler way how to specify autoreflexive attitudes were labels.Autoreflexive reasoning implemented in terms of similarity functions and close neighbourhood chunks is a more advanced form of autoreflexive attitudes.
In the preceding section we described how this kind of autoreflexive reasoning can enable a transfer from subjective to less or more intersubjective meanings.In general, we consider autoreflexive reasoning an important step towards intersubjective meanings.It is well known that autoreflexive reasoning enables to create hypotheses about the mental states of other agents (a theory of mind) [40].
Consider communication and cooperation of agents (without a language capability).Again, observations of success or failure of some actions fired in a process of communication/cooperation lead to mutual tuning of meanings (rules, situation and event types, distinguishing criteria) [41].
Next, we note that there are physical conditions for acquiring similar meanings, i.e., agents with similar "bodies" (similar anatomic, physiologic and genetic dispositions are determined to have similar subjective meanings, if they live and act in an environment of a common type. Finally, we mention an exceptionally effective role of a language on the way to intersubjective meanings.A detailed investigation of this topic is one of our future goals, but it should be noted that most of our past works were devoted to the distinguishing criteria semantics in a relation to a language in general (to languages with different levels of complexity) or to a language acquisition (see e.g.[18,19,22,25]).
Our attention is focused on a semantic treatment of verbs and sentences in order to overcome simplifications of logical or linguistic semantics.A way based on schemata of situations and events is proposed.As a consequence, we can characterize a situation based meanings of some sentences without a clear reference to some external objects.
Finally, it should be noticed that a plenty of meanings (distinguishing criteria and schemata) are introduced in terms of a language.We can speak about intersubjectivity modulo vagueness of a natural language.

INSTRUMENTS
In this section a tool is introduced which models an intersubjectivity of meanings beyond the limits of natural language with an inherent vagueness.However, it should be noticed that a natural language has a potential of bootstrapping such levels of intersubjectivity which overcome a common use of the natural language.
We model intersubjective meanings (distinguishing criteria and schemata) in terms of a measure, which is generally accessible, interpretable in a unique way and accepted by a group of agents.We will call it instrument.
Some comments are needed.First we focus on the acceptance by a group of agents.Dogmata recorded in some texts with an officially codified status and interpretation may be accepted by a group of agents, but not by another group.This is not only the case of dogmata; measurements were instruments verifying truth of geometrical claims for old Egyptian experts in geometry.A proof of geometrical claims was an acceptability instrument for ancient Greeks.
A selection of an instrument may be considered a cognitive paradigm.Let us consider Elements by Euclid [42].We may assume that Euclid believed that his own axiomatization of geometry is an embodiment of a pattern of human thinking, and he chose this pattern as a paradigm for a presentation of the knowledge of geometry.
Second, a general accessibility of an instrument is a natural conditionif an instrument should play a role of a tool of intersubjectivity for a group of agents, then an access to the instrument for each member of the group must be guaranteed.
Third, an interpretation of an instrument in an unambiguous way is an important condition, which requires a deeper analysis.
At least two levels of this condition may be distinguished.An interpretation of the instrument may be based on a mechanical procedure, on an algorithm as an extreme case, which evaluates the value of the instrument for given inputs.A simple example of such instrument is a multiplication algorithm or a cooking recipe (we will discuss examples in more detail below).However, there is also a less strict possibility.A group of agents is equipped with advanced knowledge and (reasoning) methods, which enable answer questions reliably.Distinguishing of a malign tumour by a histologist is an example of this.In an ideal case, all (good) histologists should diagnose a case of a malign tumour equivocally. 19  Let us proceed to a more formal account of instruments.A function, which represents a distinguishing criterion equipped by an instrument, has an additional argument, which denotes the instrument.The value of the function is computed (determined) according to the instrument.The weight of an object may serve as an example.An example of a distinguishing criterion with a non-algorithmic instrument is an atlas of mushrooms.
Instead of a subjective similarity function and an induced close neighbourhood relation of distinguishing criteria, thanks to instruments we can obtain exact transformations between distinguishing criteria, e.g. from kilograms to pounds.
It is obvious that distinguishing criteria are made more precise by instruments.
Schemata with instruments require a more elaborated description.We start with an example.Imagine a situation type, which represents the multiplication operation on natural numbers.The schema may contain a ternary hyperedge assigning a result to two operands.The role of vertices (operand or result) is specified by a label. 20In general, labels may specify different roles of vertices connected by a hyperedge in an arbitrary schema.A finite set of correct (true) instances of this schema may be generated by an instrumenta transformer associated with the well-known table.
The infinite set of all true instances may be generated, e.g. by a recursive definition of the multiplication.The table and the recursive definition play the role of instruments in our semantics.Both the table and the recursive definition are parts of the knowledge base.The first one can be represented as a set of hyperedges connecting three vertices labelled by two operands and one result.The second one is discussed as follows.Our goal is to represent the following two equations by a transformer and an associated situation schema: x.0 = 0 (4) x.s(y) = (x.y)+ x ( The schema may contain two hyperedges: one with two occurrences of vertices labelled by 0 and one occurrence of an unlabelled vertex.This hyperedge corresponds to formula (4) and represents the base case of the recursion.The second hyperedge corresponds to formula (5) and represents the recursive case.It connects an unlabelled vertex (corresponding to x), then a vertex (corresponding to s(y)) connected by an edge to the access point of another schema, which assigns a predecessor to a given number, and, finally, the third vertex (result) connected by an edge back to the (access point of the) multiplication schema and by another edge to the access point of an addition schema.The transformer realizes a recursive algorithm for an arbitrary pair of natural numbers and generates a situation schemaa true instance of the schema of the situation type, e.g. an instance that contains a hyperedge with vertices labelled by 2, 3 and 6.For example, the transformer first performs pattern matching that reduces the problem to series of more elementary problems (2.2, 2.1, 2.0) and finally it halts on the case 2.0=0.On the way back, it computes the series of additions (0+2+2+2=6).
A decision about a malign tumour by a histologist was mentioned as an example of a nonalgorithmic instrument.We can imagine the instrument used by a histologist as a situation schema with a vertex labelled as tumour and a set of edges with target vertices labelled by the relevant histological properties of malign tumours.Some other labels may be assigned to those verticesthey contain a description of the corresponding property in a language.Moreover, some other means of expression may be used: e.g.some properties are optional, some obligatory (this corresponds to a possibility to introduce partial properties which were discussed before).This expressivity may be added by operators labelling the corresponding edges.Sometimes also some (generalized) quantifiers applied to a set of edges might be used: for example, at least m of n properties should be present (general and existential quantifiers are special cases).
To sum-up: A distinguishing criterion with an instrument is a function with a parameter that specifies how to compute its value for its arguments.The parameter is called instrument and it is a transformer.The transformer is either an algorithm or a conventional, more or less mechanical, procedure based on an expert knowledge.In the latter case, the expert knowledge is expressed by a set of schemata associated with the transformer (as its additional arguments).A schema generated by transformer and a set of associated schemata will be called schema with an instrument.Some final remarks: A precise notion of an identity of meanings can be based on transformers defined on instruments.Sometimes rather subtle tools are needed.
An optional specification of a group of agents can be added as an argument to a distinguishing criterion with an instrument.
A specification of a group of agents in a schema may serve as an example of meta-level features of schemata, e.g. a schema may be connected by an edge labelled e.g. as "owner" to a vertex labelled by an identification of a group of agents.

CONCLUSIONS MAIN CONTRIBUTIONS
Building on our previous works, we have proposed a semantic framework with meanings connected to cognitive agents, rooted in their experience and separable from language, covering a wide spectrum of cognitions ranging from living organisms (animals, pre-verbal children and adult humans) to artificial agents (softbots, robots, multi-agent systems etc.)In this article, we substantially revised our previous conception of distinguishing criteria (added transformers and constructors), enriched the framework with schemata, knowledge base, beliefdesireintention structures and other constructs (for their full list, see Appendix A).
An interesting property of the proposed semantics is that it enables coexistence of subjective and intersubjective meanings.Subjective (the first person perspective) meanings are primary, and we have shown the way from them to collectively accepted (the third person perspective) meanings via observable behaviour and feedback about success/failure of actions and instruments.We have defined the notion of truth in a similar way.This is a novel and previously unpublished contribution.

OPEN PROBLEMS AND FUTURE RESEARCH
First of all, the proposed semantic framework is in many respects still a blueprint, especially in terms of a proper mathematical formalization.A more detailed, deeper and more precise analysis of the features of our semantics is needed; together with an argumentation that the features are really satisfied and an attempt to argue that those features should be satisfied by each cognitive semantics that aspires to be biologically relevant.
Regarding particulars, construction of more complex schemata as rules, a more detailed reconstruction of reaching an approximate truth with subjective meanings and an elaboration of the idea of instrument are necessary.
It is also needed to elaborate details of the relation of the proposed semantic constructs to natural language and particular linguistic constructions, e.g.define semantics of verbs and propositions, and analyse the role of natural language on the way to intersubjective meanings.
We also plan to tell a developmental story in more detailhow can an agent construct/learn schemata and distinguishing criteria from experience.The theory calls for empirical evaluation in terms of analyses of animal behaviour, child development studies and psychological experiments.It should also be supported by computational models and their simulations.Regarding instruments, it would be interesting to come up with particular case studies of methodologies and paradigm shifts in the history of science.
Our future plans further include enhancing schemata and distinguishing criteria with affective values (possibly based on previous success/failure or reinforcement), elaboration of the agent's motivational system, detailed formalization of (non-monotonic) reasoning within this framework, including fast reasoning (jumping to conclusions).
Despite these open issues, we have identified an important research direction and have taken first steps toward more biologically relevant semantic theory.We believe that this theory has a potential to address several current issues in linguistics, logic, cognitive science and philosophy of science, with possible interesting applications in artificial intelligence, adaptive knowledge representation, machine learning and cognitive modeling. 15The research in machine learning and artificial neural networks has yielded many good ideas how to extract knowledge from examples by mostly uninformed statistical calculations [37,38]. 16In the past, we have successfully formalized and implemented distinguishing criteria as similarity functions each with their own Mahalanobis metric with parameters induced from statistical characteristics of the exemplars [22]. 17Constructors can also modify an existing detector when new exemplars arrive. 18The function only returns a value for some inputs; it is undefined for others, which can be interpreted as a "don't know" value. 19However, in fact this condition is rarely satisfied.With non-algorithmic instruments, there is always a possibility of alternative (mis)interpretations.In our example with a case of malign tumour, all interpretations that misdiagnose a malign tumour as benign are considered incorrect. 20Depending on the labels specifying which vertices have numerical values assigned, the same schema can be used for multiplication, division, or checking the truth of the corresponding statement.
zooming in/out, etc. Action rule A type of a rule associated with an action (overt behaviour); the rule specifies the prerequisites and consequences of the action execution.Goal A desired situation -a situation schema labelled with the autoreflexive attitude "goal".Plan A chain of rules supposedly leading to the fulfilment of a goal.

Routine
A plan successful in the past.

Distinguishing criterion with an instrument
A function with an instrument parameter; the parameter specifies a transformer able to compute the value of the function.

Schema with an instrument
A schema generated by a transformer (an algorithm or a conventional, rather mechanical procedure, based on an expert knowledge) and a set of associated schemata.
It t = (Beh t )observed behaviour in a time point t. , P'(Env t ), B' t , D' t , I' t )all components marked with ' are constructed by abduction based on the Me's own knowledge (theory of mind).Complete view of another agent It' t = (KB' t , P'(Env t ), B' t , D' t , I' t , Beh t ). t