Truth-value Semantics Research Articles

How semantics works in Chinese relative clause processing: insights from eye tracking.

Recent years have witnessed much research on semantic analysis and syntactic anatomy in ordinary language processing. However, it is still a matter of considerable debate about when and how the semantic integration of single word meanings works and interacts with syntax during on-line comprehension. This study, in an eye-tracking paradigm, took 38 native speakers of Mandarin Chinese as the participants and took Chinese relative clauses as stimuli to figure out the functions of semantics by investigating the conditioning semantic factors influencing and governing the word order variation of Chinese relative clauses during different processing stages. Accordingly, this study manipulated two syntactic variables, i.e., relative clause type and the position of the numeral-classifier sequence (NCL) in the relative clause, as well as a semantic variable, i.e., the abstractness of the head noun that the relative clause modified. Specifically, the study addressed two questions: (1) when semantics is activated and interacts with syntax and (2) how semantics affects syntax during the time course of Chinese relative clause processing. The results indicated that: (1) Semantics was activated and interacted with syntax during the early and late processing stages of Chinese relative clauses, which challenged the sequential order of syntactic and semantic processes, and supported the claims of the Concurrent Processing Model. (2) The syntactic order of the Chinese relative clause was affected by the semantic information of the head noun that the clause modified. Object-extraction relative clauses (ORCs) had a conjunction preference for the order "an object relative clause preceding the numeral-classifier sequence and the head noun." Instead, the subject-extraction relative clause (SRC) which modified a concrete noun (CN) had a co-occurrence preference for the order "numeral-classifier sequence preceding the subject relative clause and the head noun," while the subject-extraction relative clause which modified an abstract noun (AN) had a co-occurrence preference for the order "subject relative clause preceding the numeral-classifier sequence and the head noun." The findings of this study were evaluated in light of the perspectives of truth value semantics of the syntactic components, the semantic compatibility of numeral-classifier sequence and its modified noun as well as the discourse functions of outer modifier nominals and inner modifier nominals.

真值语义相同下的“才”和“就”之比较

真值语义相同下的“才”和“就”之比较

Same Same But Different: An Alphabetically Innocent Compositional Predicate Logic

Compositionality is at the heart of model theoretical semantics, and the most common way of doing truth value semantics for natural language (NL) is to translate a fragment of NL into some extensions of classical predicate logic. Yet, somewhat ironically and strangely enough, predicate logic itself is not compositional, because the truth conditions for quantification as usually stated are not a function of the denotations of its parts but depend on value assignments for variables. That this kind of dependence on value assignments leads to non-compositionality is well-known and will be demonstrated explicitly in section 1.3. One could, as is also well-known, remedy this awkwardness by considering not truth values as denotations of formulas but sets of value assignments for variables. As we will show in 1.4, such a semantics is compositional, but now an additional problem emerges, namely the lack of alphabetical “innocence” (or “invariance”) in that the denotation of P(x) is different from that of P(y) although the formulas are mere alphabetic variants of each other.1 This new problem is related to what Fine (2007), p. 7, calls the “antinomy of the variable”:

Truth-Value Semantics and Functional Extensions for Classical Logic of Partial Terms Based on Equality

We develop a bottom-up approach to truth-value semantics for classical logic of partial terms based on equality and apply it to prove the conservativity of the addition of partial description and partial selection functions, independently of any strictness assumption.

Associative Substitutional Semantics and Quantified Modal Logic

The paper presents an alternative substitutional semantics for first-order modal logic which, in contrast to traditional substitutional (or truth-value) semantics, allows for a fine-grained explanation of the semantical behavior of the terms from which atomic formulae are composed. In contrast to denotational semantics, which is inherently reference-guided, this semantics supports a non-referential conception of modal truth and does not give rise to the problems which pertain to the philosophical interpretation of objectual domains (concerning, e.g., possibilia or trans-world identity). The paper also proposes the notion of modality de nomine as an alternative to the denotational notion of modality de re.

State-of-affairs Semantics for Positive Free Logic

In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain–outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails.

On phase semantics and denotational semantics: the exponentials

We extend to the exponential connectives of linear logic the study initiated in Bucciarelli and Ehrhard (Ann. Pure. Appl. Logic 102 (3) (2000) 247). We define an indexed version of propositional linear logic and provide a sequent calculus for this system. To a formula A of indexed linear logic, we associate an underlying formula A ̄ of linear logic, and a family 〈A〉 of elements of | A ̄ | , the interpretation of A ̄ in the category of sets and relations. Then A is provable in indexed linear logic iff the family 〈A〉 is contained in the interpretation of some proof of A ̄ . We extend to this setting the product phase semantics of indexed multiplicative additive linear logic introduced in Bucciarelli and Ehrhard (2000), defining the symmetric product phase spaces. We prove a soundness result for this truth-value semantics and show how a denotational model of linear logic can be associated to any symmetric product phase space. Considering a particular symmetric product phase space, we obtain a new coherence space model of linear logic, which is non-uniform in the sense that the interpretation of a proof of !A−∘B contains informations about the behavior of this proof when applied to “chimeric” arguments of type A (for instance: booleans whose value can change during the computation). In this coherence semantics, an element of a web can be strictly coherent with itself, or two distinct elements can be “neutral” (that is, neither strictly coherent, nor strictly incoherent).

On phase semantics and denotational semantics in multiplicative–additive linear logic

We study the notion of logical relation in the coherence space semantics of multiplicative-additive linear logic MALL . We show that, when the ground-type logical relation is “closed under restrictions”, the logical relation associated to any type can be seen as a map associating facts of a phase space to families of points of the web of the corresponding coherence space. We introduce a sequent calculus extension of MALL whose formulae denote these families of points. This logic MALL(I) (where I is a set of indexes) admits a truth-value semantics in the previously mentioned phase space, and this truth-value semantics faithfully describes the logical relation model we started from. Then we generalize this notion of phase space, we prove a truth-value completeness result for MALL(I) and we derive from any phase model of MALL(I) a denotational model for MALL . Using the truth-value completeness result, we obtain a weak denotational completeness result based on this new denotational semantics.

Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic

AbstractSome of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917–1923. The aim of this paper is to describe these results, focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic (“Post-”) and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged.

Henkin's completeness proof: forty years later.

1 In his 1949 paper, completeness of the first-order calculus, Henkin developed what is now called the method of (individual) terms to establish that every consistent set of statements of a first-order language L a model of cardinality α, a the number of statements of L. The idea is to start with such a set S, construct a so-called term-extension L of L by adding a new terms to the vocabulary of L, extend 5 to a maximally consistent and term-complete set Soo of statements of L, and construct a model of S& whose domain consists of the terms of L. When restricted to L, the model in question automatically constitutes one of S. Henkin's result come to be known as the Strong Completeness Theorem for First-Order L. Another, and more familiar, version of the theorem it that if a statement A ofL is true in every model of a set S of statements ofL, then A is provable from S. Henkin himself did not bother to prove this. He merely proved the special case of it, known as the Weak Completeness Theorem for First-Order L9 where S is 0 . A model like the one Henkin constructed for his set Ŝ , is commonly known as a Henkin model. It is the kind of model in which each member of the domain has a name. Henkin accomplished this by making each member of his domain a name of itself, a radical move at the time. In consequence, though, the restriction of his model to L does not constitute a Henkin model of S, a pity in the event that S does have such a model. To commemorate the publication of Henkin's paper, we offer here two new completeness proofs for first-order Z,. The language considered by Henkin had an unspecified number of terms to start with, but those played no special role in his proof. The one we construct in Section 2 denumerably many, and these will play a crucial role in our proofs. In the first of them, begun in Section 3 and concluded in Section 5, no new terms will be added; in the second, presented in Section 5 and relating to truth-value semantics, denumerably many will be. The proofs are sharpenings of proofs of Leblanc's in [10]. They have two cases each, Case One minding the consistent sets of statements of L that extend without the

Semantics without reference.

A theory of reference may be either an analysis of reference or merely an account of the correct use of the verb «to refer». If we define the validity of arguments in the standard way, in terms of assignments of individuals and sets to the nonlogical vocabulary of the language, then, it is argued, we will be committed to seeking an analysis of reference. This paper shows how validity (i.e., semantic consequence) may be defined in a way that avoids the problems facing other alternatives to standard semantics and also permits a metalinguistic account of reference. The validity of arguments is treated as a matter of logical form, but validity for forms is defined on analogy with the definition of semantic consequence in truth-value semantics

Hugues Leblanc. Preface. Existence, truth, and provability, by Hugues Leblanc, State University of New York Press, Albany1982, pp. ix–x. - Hugues Leblanc. Introduction. Existence, truth, and provability, by Hugues Leblanc, State University of New York Press, Albany1982, pp. 3–16. - Hugues Leblanc and T. Hailperin. Non-designating singular terms. A revised reprint of XXV 87. Existence, truth, and provability, by Hugues

Hugues Leblanc. Preface. Existence, truth, and provability, by Hugues Leblanc, State University of New York Press, Albany1982, pp. ix–x. - Hugues Leblanc. Introduction. Existence, truth, and provability, by Hugues Leblanc, State University of New York Press, Albany1982, pp. 3–16. - Hugues Leblanc and T. Hailperin. Non-designating singular terms. A revised reprint of XXV 87. Existence, truth, and provability, by Hugues

Nominalism and conceptualism as predicative second-order theories of predication.

There appears to be a growing consensus, even if not unanimity, that standard predicative second-order logic is the appropriate logical medium for the representation of a nominalist theory of predication.* We agree that this is indeed the case and formulate in this paper a model-theoretic approach which justifies that claim.* Because it is model-theoretic, our approach differs from the truth-value semantics approach of Leblanc and Weaver. Amongst other reasons, we prefer our model-theoretic approach so as to accommodate those nominalists for whom the assumption that there are potentially as many names as there are individuals is not acceptable. The models involved in our semantics, moreover, are precisely the same models as are already involved in standard first-order logic. Assignments of values (drawn from the domain of a given model) to the individual variables are extended, however, to what, relative to a given first-order language, we call nominalistic assignments to the π-place predicate variables (for each positive integer ή) these assign first-order formulas (wffs) of the language in question, relative to the free occurrences of n distinct individual variables occurring in those wffs, to the H-place predicate variables. The satisfaction by such an assignment of a second-order wff in a model is then defined by a double recursion on the logical structure of the wff and on the number of nested predicate quantifiers occurring therein.

J. Michael Dunn. A truth value semantics for modal logic. Truth, syntax and modality, Proceedings of the Temple University Conference on Alternative Semantics, edited by Hugues Leblanc, Studies in logic and the foundations of mathematics, vol. 68, North-Holland Publishing Company, Amsterdam and London1973, pp. 87–100.

J. Michael Dunn. A truth value semantics for modal logic. Truth, syntax and modality, Proceedings of the Temple University Conference on Alternative Semantics, edited by Hugues Leblanc, Studies in logic and the foundations of mathematics, vol. 68, North-Holland Publishing Company, Amsterdam and London1973, pp. 87–100.

Truth-value semantics for a logic of existence.

Truth-value semantics for a logic of existence.