Abstract
Part I presented the basic mechanism of natural communication using the example of a talking robot. Part II explained the complexity-theoretic aspects of syntactic analysis. Part III developed detailed morphological and syntactic analyses of natural language surfaces. Based on these foundations, we turn in Part IV to the semantic and pragmatic interpretation of syntactically analyzed expressions in natural language interpretation and production.
First, traditional approaches to semantic interpretation will be described in Chaps. 19–21, explaining basic notions, goals, methods, and problems. Then a semantic and pragmatic interpretation of LA Grammar within the Slim theory of language will be developed in Chaps. 22–24. The formal interpretation is implemented computationally as a content-addressable database system called a word bank.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
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 it would be extremely susceptible to error.
- 2.
In the sense of always going from true premises to true conclusions.
- 3.
An early highlight is the writing of Aristotle, in which logical variables are used for the first time.
- 4.
Scott and Strachey (1971).
- 5.
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 (Weyhrauch 1980). This requirement has already modified modern approaches to proof theory profoundly (P→L reconstruction).
- 6.
Sect. 19.4.
- 7.
For simplicity, we do not use here a recursive definition of syntactic categories with systematically associated semantic types à la Montague (CoL, pp. 344–349).
- 8.
Tarski (1944) complains about these misunderstandings and devotes the second half of his paper to a detailed critique of his critics.
- 9.
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 \(\mathcal{M}\). In a world where it is snowing only at certain times and certain places, on the other hand, 19.3.5 will work only if the interpretation of the sentence is restricted – at least implicitly – to an intended location and moment of time.
- 10.
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.
- 11.
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 kinds 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 kinds 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.
- 12.
See in this connection also 3.4.5.
- 13.
CoL, pp. 307f.
- 14.
With the notable exception of propositional calculus. See also transfer in 19.2.3.
- 15.
For a detailed analysis of the weak version(s) see Thiel (1995), pp. 325–327.
- 16.
The page and line numbers have been adjusted here from Tarski’s original text to fit those of this chapter. This adjustment is crucial in order for self-reference to work.
- 17.
- 18.
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.
- 19.
Montague (1974), p. 188.
- 20.
As a compromise, Davidson suggested limiting the logical semantic analysis of natural language to suitable consistent fragments of natural language. This means, however, that the project of a complete logical semantic analysis of natural languages is doomed to fail.
Attempts to avoid the Epimenides paradox in logical semantics are Kripke (1975), Gupta (1982), and 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 Epimenides paradox, which is essentially a problem of reference: a symbol may refer on the basis of its meaning and at the same time serve as a referent on the basis of its form.
- 21.
As an L→N reconstruction (19.2.3).
References
Davidson, D. (1967) “Truth and Meaning,” Synthese VII:304–323
Frege, G. (1892) “Über Sinn und Bedeutung,” Zeitschrift für Philosophie und philosophische Kritik 100:25–50
Gupta, A. (1982) “Truth and Paradox,” Journal of Philosophical Logic 11:1–60
Herzberger, H. (1982) “Notes on Naive Semantics,” Journal of Philosophical Logic 11: 61–102
Kripke, S. (1975) “Outline of a Theory of Truth,” The Journal of Philosophy 72:690–715
Montague, R. (1974) Formal Philosophy, New Haven: Yale University Press
Pascal, B. (1951) Pensées sur la Religion et sur Quelques Autre Sujets, Paris: Éditions du Luxembourg
Scott, D., and C. Strachey (1971) “Toward a Mathematical Semantics of Computer Languages,” Technical Monograph PRG-6, Oxford University Computing Laboratory, Programming Research Group, 45 Branbury Road, Oxford, UK
Tarski, A. (1935) “Der Wahrheitsbegriff in den formalisierten Sprachen,” Studia Philosophica I:262–405.
Tarski, A. (1944) “The Semantic Concept of Truth,” Philosophy and Phenomenological Research 4:341–375
Thiel, C. (1995) Philosophie und Mathematik, Darmstadt: Wissenschaftliche Buchgesellschaft
Weyhrauch, R. (1980) “Prolegomena to a Formal Theory of Mechanical Reasoning,” Artificial Intelligence, reprint in Webber and Nilsson (eds.), 1981
Author information
Authors and Affiliations
Exercises
Exercises
Section 19.1
-
1.
What areas of science deal with semantic interpretation?
-
2.
Explain the basic structure common to all systems of semantic interpretation.
-
3.
Name two practical reasons for building semantic structures indirectly via the interpretation of syntactically analyzed surfaces.
-
4.
Explain the inverse procedures of representation and reconstruction.
-
5.
How many kinds of semantic interpretation can be assigned to a given language?
-
6.
Explain in what sense axiomatic systems of deduction are not true systems of semantic interpretation.
Section 19.2
-
1.
Describe three different kinds of formal semantics.
-
2.
What is the function of syntactically analyzed surfaces in the programming languages?
-
3.
What principle is the semantics of the programming languages based on and how does it differ from that of the logical languages?
-
4.
What is the basic difference between the semantics of the natural languages, on the one hand, and the semantics of the logical and the programming languages, on the other?
-
5.
Why is a syntactical analysis presupposed by a formal semantic analysis?
-
6.
Discuss six possible relations between different kinds of semantics.
-
7.
What kinds of difficulties arise in the replication of logical proof theory in the form of computer programs for automatic theorem proving?
Section 19.3
-
1.
Name the components of a model theoretically interpreted logic and explain their functions.
-
2.
What are the goals of logical semantics?
-
3.
What is Tarski’s T-condition and what is its purpose for semantic interpretation?
-
4.
Why is verification a central part of Tarski’s theory of truth?
-
5.
What is the role of translation in Tarski’s T-condition?
-
6.
Why does Tarski construct the metalanguage in his example of the calculus of classes? What notions does he use in this construction?
-
7.
What does immediate obviousness do for verification in mathematical logic?
Section 19.4
-
1.
Explain a vacuous T-condition with an example.
-
2.
What is the potential role of non-mathematical sciences in Tarski’s theory of truth?
-
3.
For what purpose does Tarski construct an infinite hierarchy of metalanguages?
-
4.
Why is the method of metalanguages unsuitable for the semantic interpretation of programming languages?
-
5.
What is the precondition for realizing a logical calculus as a computer program?
-
6.
In what sense does Tarski’s requirement that only immediately obvious notions be used in the metalanguage have a counterpart in the procedural semantics of the programming languages?
Section 19.5
-
1.
How does Tarski view the application of logical semantics to the analysis of natural languages?
-
2.
Explain the Epimenides paradox.
-
3.
Explain the three options for avoiding the inconsistency of logical semantics caused by the Epimenides paradox.
-
4.
What is the difference between a false logical proposition like ‘A & ¬A’ and a logical inconsistency caused by a paradox?
-
5.
What difference does Montague see between the artificial and the natural languages, and what is his goal in the analysis of natural languages?
-
6.
Give three reasons for applying logical semantics to natural languages. Are they valid?
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hausser, R. (2014). Three Kinds of Semantics. In: Foundations of Computational Linguistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41431-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-41431-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-41430-5
Online ISBN: 978-3-642-41431-2
eBook Packages: Computer ScienceComputer Science (R0)