A skeptical theory of inheritance in nonmonotonic semantic networks

doi:10.1016/0004-3702(90)90057-7

Artificial Intelligence

Volume 42, Issues 2–3, March 1990, Pages 311-348

https://doi.org/10.1016/0004-3702(90)90057-7 Get rights and content

Abstract

This paper describes a new approach to inheritance reasoning in semantic networks allowing for multiple inheritance with exceptions. The approach leads to an analysis of defeasible inheritance which is both well-defined and intuitively attractive: it yields unambiguous results applied to any acyclic semantic network, and the results conform to our intuitions in those cases in which the intuitions themselves are firm and unambiguous. Since the definition provided here is based on an alternative, skeptical view of inheritance reasoning, however, it does not always agree with previous definitions when it is applied to nets about which our intuitions are unsettled, or in which different reasoning strategies could naturally be expected to yield distinct results. After exploring certain features of the definition presented here, we describe also a hybrid (parallel-serial) algorithm that implements the definition in a parallel marker-passing architecture.

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A representational limitation of current argumentation frameworks is their inability to deal with sets of entities and their properties, for example to express that an argument is applicable for a specific set of entities that have a certain property and not applicable for all the others. In order to address this limitation, we recently introduced Abstract Argumentation Frameworks with Domain Assignments (AAFDs), which extend Abstract Argumentation Frameworks (AAFs) by assigning to each argument a domain of application, i.e., a set of entities for which the argument is believed to apply. We provided formal definitions of AAFDs and their semantics, showed with examples how this model can support various features of commonsense and non-monotonic reasoning, and studied its relation to AAFs. In this paper, aiming to provide a deeper insight into this new model, we present more results on the relation between AAFDs and AAFs and the properties of the AAFD semantics, and we introduce an alternative, more expressive way to define the domains of arguments using logical predicates. We also offer an implementation of AAFDs based on Answer Set Programming (ASP) and evaluate it using a range of experiments with synthetic datasets.
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It is reasonable to assume that a particular bird, Tweety, flies, unless it is an exceptional bird: ostrich, duck, penguin, and so on [2]. This type of reasoning can be modelled in AI by several non-monotonic formalisms [1], such as inheritance networks with exception [7], semantic networks using Dempster’s rule [8], non-monotonic logics [4,9,10] and knowledge-based systems [11]. Still, to the best of the authors’ knowledge, there is an absence in the literature of empirical comparisons among some of these formalisms.
Dealing with uncertain, contradicting, and ambiguous information is still a central issue in Artificial Intelligence (AI). As a result, many formalisms have been proposed or adapted so as to consider non-monotonicity. A non-monotonic formalism is one that allows the retraction of previous conclusions or claims, from premises, in light of new evidence, offering some desirable flexibility when dealing with uncertainty. Among possible options, knowledge-base, non-monotonic reasoning approaches have seen their use being increased in practice. Nonetheless, only a limited number of works and researchers have performed any sort of comparison among them. This research article focuses on evaluating the inferential capacity of defeasible argumentation, a formalism particularly envisioned for modelling non-monotonic reasoning. In addition to this, fuzzy reasoning and expert systems, extended for handling non-monotonicity of reasoning, are selected and employed as baselines, due to their vast and accepted use within the AI community. Computational trust was selected as the domain of application of such models. Trust is an ill-defined construct, hence, reasoning applied to the inference of trust can be seen as non-monotonic. Inference models were designed to assign trust scalars to editors of the Wikipedia project. Scalars assigned to recognised trustworthy editors provided the basis for the analysis of the models’ inferential capacity according to evaluation metrics from the domain of computational trust. In particular, argument-based models demonstrated more robustness than those built upon the baselines despite the knowledge bases or datasets employed. This study contributes to the body of knowledge through the exploitation of defeasible argumentation and its comparison to similar approaches. It provides publicly implementations for the designed models of inference, which might be a useful aid to scholars interested in performing non-monotonic reasoning activities. It adds to previous works, empirically enhancing the generalisability of defeasible argumentation as a compelling approach to reason with quantitative data and uncertain knowledge.
An empirical evaluation of the inferential capacity of defeasible argumentation, non-monotonic fuzzy reasoning and expert systems
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Many non-monotonic reasoning formalisms exist in Artificial Intelligence (Brewka, 1991). For instance inheritance networks with exception (Horty, Thomason, & Touretzky, 1990) or semantic networks using Demptster’s rule (Ginsberg, 1984). Other examples include non-monotonic logics like circumscription (McCarthy, 1980), autoepistemic (Moore, 1985) and default logic (Reiter, 1980).
Several non-monotonic formalisms exist in the field of Artificial Intelligence for reasoning under uncertainty. Many of these are deductive and knowledge-driven, and also employ procedural and semi-declarative techniques for inferential purposes. Nonetheless, limited work exist for the comparison across distinct techniques and in particular the examination of their inferential capacity. Thus, this paper focuses on a comparison of three knowledge-driven approaches employed for non-monotonic reasoning, namely expert systems, fuzzy reasoning and defeasible argumentation. A knowledge-representation and reasoning problem has been selected: modelling and assessing mental workload. This is an ill-defined construct, and its formalisation can be seen as a reasoning activity under uncertainty. An experimental work was performed by exploiting three deductive knowledge bases produced with the aid of experts in the field. These were coded into models by employing the selected techniques and were subsequently elicited with data gathered from humans. The inferences produced by these models were in turn analysed according to common metrics of evaluation in the field of mental workload, in specific validity and sensitivity. Findings suggest that the variance of the inferences of expert systems and fuzzy reasoning models was higher, highlighting poor stability. Contrarily, that of argument-based models was lower, showing a superior stability of its inferences across knowledge bases and under different system configurations. The originality of this research lies in the quantification of the impact of defeasible argumentation. It contributes to the field of logic and non-monotonic reasoning by situating defeasible argumentation among similar approaches of non-monotonic reasoning under uncertainty through a novel empirical comparison.
Rethinking specificity in defeasible reasoning and its effect in argument reinstatement
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Hempel [19] defended a requirement of maximal specificity as a condition for the acceptance of probabilistic or inductive-statistical explanations. Early applications of specificity in non-monotonic reasoning in AI were also aware of the intuition that only maximally specific explanations should be accepted, so from the argumentative point of view [29] as from the defeasible inheritance networks point of view [14,15,23,32]. Nevertheless, all of these approaches suffer some of the mentioned problems.
The principle of reinstatement governing most argument systems states that an argument is reinstated when all its defeaters are in turn ultimately defeated. Nevertheless, some criticisms to this principle have been offered in the literature. We found that problems arise when arguments in a chain of attacks are related by specificity: when non-maximally specific arguments are reinstated, fallacious justifications are originated. Particularly, we show how the problem affects DeLP, a system that combines a specificity-based defeat criterion with a reinstatement-based warrant process. Following old intuitions by philosopher Carl Hempel we rethink the concept's role within defeasible argumentation. Two kinds of specificity defeaters are identified: proper defeaters and cautious defeaters. While proper defeaters are well-known, cautious defeaters are formally introduced here. A system combining cautious and proper defeaters is defined as an extension of DeLP, and dialectic warrant games are proposed for filtering out non-maximally specific arguments.
Making the right exceptions
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Citation Excerpt :
The question is whether Nixon is Anti-military. In preemption based approaches (notably Horty et al. [3]), the positive path from N to A is disabled by the negative path from N to P, so that ¬A may be concluded. This outcome is considered counterintuitive since the negative path to A is itself disabled by its positive counterpart, which is why such paths are referred to as zombie paths. (
This paper is about the logical properties of sentences of the form S's are normally P, and starts from the idea that any logical theory for such sentences should meet the following simple requirement:
If the only available information about some object x is that x has property S, it must be valid to infer by default that x has all the properties P that objects with property S normally have.
We investigate how this requirement can be met by theories developed within the framework of circumscription, and specify a constraint – the exemption principle – that must be satisfied to do so. This principle determines in cases of conflicting default rules which objects are exempted from which rules, and, as such, is the main source for the capricious logical behavior of the sentences we are interested in.
To facilitate comparison (and implementation) we supply an algorithm for inheritance networks and prove that arguments that can be expressed in both frameworks are valid on the circumscriptive account if and only if the inheritance algorithm has a positive outcome.
Defeasible inheritance with doubt index and its axiomatic characterization
2010, Artificial Intelligence
This article introduces and uses a representation of defeasible inheritance networks where links in the network are viewed as propositions, and where defeasible links are tagged with a quantitative indication of the proportion of exceptions, called the doubt index. This doubt index is used for restricting the length of the chains of inference.
The representation also introduces the use of defeater literals that disable the chaining of subsumption links. The use of defeater literals replaces the use of negative defeasible inheritance links, expressing “most A are not B”. The new representation improves the expressivity significantly.
Inference in inheritance networks is defined by a combination of axioms that constrain the contents of network extensions, a heuristic restriction that also has that effect, and a nonmonotonic operation of minimizing the set of defeater literals while retaining consistency.
We introduce an underlying semantics that defines the meaning of literals in a network, and prove that the axioms are sound with respect to this semantics. We also discuss the conditions for obtaining completeness.
Traditional concepts, assumptions and issues in research on nonmonotonic or defeasible inheritance are reviewed in the perspective of this approach.

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A skeptical theory of inheritance in nonmonotonic semantic networks

Abstract

Artificial Intelligence

Artificial Intelligence

Artificial Intelligence

Artificial Intelligence

How a computer should think

A useful four-valued logic

Generic terms and generic sentences

J. Philos. Logic

NETL: A System for Representing and Using Real-World Knowledge

Design sketch for a million-element NETL machine

Cancellation in a parallel semantic network

The Connection Machine