Abstract
Part I presented the mechanism of natural communication within the Slim theory of language. Part II described algorithms of generative grammar for automatically analyzing the combinatorics of formal and natural languages. Part III developed detailed morphological and syntactical analyses of natural language surfaces using the time-linear algorithm of LA-grammar. Based on these foundations, we turn in Part IV to the semantic and pragmatic interpretation of natural language.
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For example, it is much easier to handle the surfaces of an expression like 36 • 124 than to execute the corresponding operation of multiplication semantically by using an abacus. Without the language surfaces one would have to slide the counters on the abacus 36 times 124 `semantically’ each time this content is to be communicated. This would be tedious, and even if the persons communicating were to fully concentrate on the procedure each time it would be extremely susceptible to error.
An early highlight is the writing of Aristotle, where logical variables are used for the first time.
D. Scott and C. Strachey 1971.
The transfer of logical proof theory to an automatic theorem prover necessitates that each step — especially those considered `obvious’ — be realized in terms of explicit computer operations (cf. R. Weyhrauch 1980). This requirement has already modified modern approaches to proof theory profoundly (P-*L reconstruction).
Cf. Section 19.4.
For simplicity, we do not use here a recursive definition of syntactic categories with systematically associated semantic types à la Montague. Cf. CoL, p. 344–349.
A. Tarski 1944 complains about these misunderstandings and devotes the second half of his paper to a detailed critique of his critics.
Compared to 19.3.5, 19.3.6 is more precise because the interpretation is explicitly restricted to a specific state of affairs, specified formally by the model M. In a world where it snows only at certain times and certain places, on the other hand, 19.3.5 will work only if the interpretation of the sentence is limited — at least implicitly — to an intended location and moment of time.
Tarski’s own example 19.3.4 is only slightly less vacuous. This is because the metalanguage translation in Tarski’s example is in a natural language different from the object language. The metalanguage translation into another natural language is misleading, however, because it omits the aspect of verification, which is central to a theory of truth. The frequent misunderstandings which Tarski 1944 so eloquently bewails may well have been caused in large part by the `intuitive’ choice of his examples.
The discussion of Tarski’s semantics in CoL, pp. 289–295, 305–310, and 319–323, was aimed at bringing out as many similarities between the semantics of logical, programming, and natural languages as possible. For example, all three types of semantic interpretation were analyzed from the viewpoint of truth: whereas logical semantics checks whether a formula is true relative to a model or not, the procedural semantics of a programming language constructs machine states which `make the formula true,’ — and similarly in the case of natural semantics. Accordingly, the reconstruction of logical calculi on the computer was euphemistically called `operationalizing the metalanguage’. Further reflection led to the conclusion, however, that emphasizing the similarities was not really justified: because of the differing goals and underlying intuitions of the three types of semantics a general transfer from one system to another is ultimately impossible. For this reason the current analysis first presents what all semantically interpreted systems have in common, namely the basic two-level structure, and then concentrates on bringing out the formal and conceptual differences between the three systems.
See in this connection also 3.4.3.
CoL, p. 307 ff.
With the notable exception of propositional calculus. See also transfer in 19.2.3.
For a detailed analysis of the weak version(s) see C. Thiel, 1995, p. 325–7.
The page and line numbers have been adjusted from Tarski’s original text to fit those of this chapter. This adjustment is crucial in order for self reference to work.
The second option will be explored in Chapter 21, especially Section 21.2, for the semantics of natural language.
This follows from the role of natural languages as the pretheoretical metalanguage of the logical languages. Without the words true and false in the natural languages a logical semantics couldn’t be defined in the first place.
R. Montague 1974, p.188.
As a compromise, Davidson suggested to limit the logical semantic analysis of natural language to suitable consistent fragments. This means, however, that the project of a complete logical semantics for natural language is doomed to fail. Attempts to avoid the Epimenides paradox in logical semantics are S. Kripke 1975, A. Gupta 1982, and H. Herzberger 1982. These systems each define an artificial object language (first order predicate calculus) with truth predicates. That this object language is nevertheless consistent is based on defining the truth predicates as recursive valuation schemata. Recursive valuation schemata are based on a large number of valuations (transfinitely many in the case of Kripke 1975). As a purely technical trick, they miss the point of the Epimendes paradox which is essentially a problem of reference: a symbol may refer on the basis of its meaning and at the same time be a referent on the basis of its form.
As an L-3N reconstruction, cf. 19.3.3.
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© 1999 Springer-Verlag Berlin Heidelberg
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Hausser, R. (1999). Three system types of semantics. In: Foundations of Computational Linguistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03920-5_20
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