Interpreting logical form

May, Robert

doi:10.1007/bf00632471

Cited by 83 publications

(40 citation statements)

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“…is universally applicable." 27 Our analysis has led to the following solution to the problem of logical consequence. The characteristic property of logical consequence (the logical property X) is formality: logical consequences take into account formal features of objects; logical consequences preserve truth in all formally possible structures of objects.…”

Section: Does (5) Hold In Standard Semantics?mentioning

confidence: 99%

Did Tarski commit “Tarski's fallacy”?

Sher

1996

J. symb. log.

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In his 1936 paper, On the Concept of Logical Consequence, Tarski introduced the celebrated definition of logical consequence: “The sentenceσ follows logically from the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentence σ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentence σ is false. Moreover, … we are concerned here with the concept of logical, i.e., formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since.

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Section: Does (5) Hold In Standard Semantics?mentioning

confidence: 99%

Did Tarski commit “Tarski's fallacy”?

Sher

1996

J. symb. log.

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“…According to May (1989), factorization fails to respect compositionality, because part of the semantic contribution of the composing elements is simply erased. As an alternative, he defines an absorption operation which interprets a sequence of negative indefinites NO x1 , ...NO xn as a polyadic quantifier complex NO x1 ... xn (cf.…”

Section: Criteriamentioning

confidence: 99%

“…Note that absorption requires a mode of composition different from function application, so it does not respect first-order (Fregean) compositionality. However, absorption is embedded in a more general theory of polyadic quantification (May 1989, Van Benthem 1989), so it is one of a series of operations in natural language that goes beyond standard generalized quantifier theory. If we accept the set of operations defined in polyadic generalized quantifier theory as permissible combinatoric rules, May's analysis is compositional in a higher order theory of meaning.…”

Section: Criteriamentioning

confidence: 99%

Expression and Interpretation of Negation

Swart

2010

Studies in Natural Language and Linguistic Theory

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Chapter summaryThis chapter introduces the empirical scope of our study on the expression and interpretation of negation in natural language. We start with some background notions on negation in logic and language, and continue with a discussion of more linguistic issues concerning negation at the syntax-semantics interface. We zoom in on crosslinguistic variation, both in a synchronic perspective (typology) and in a diachronic perspective (language change). Besides expressions of propositional negation, this book analyzes the form and interpretation of indefinites in the scope of negation. This raises the issue of negative polarity and its relation to negative concord. We present the main facts, criteria, and proposals developed in the literature on this topic. The chapter closes with an overview of the book. We use Optimality Theory to account for the syntax and semantics of negation in a cross-linguistic perspective. This theoretical framework is introduced in Chapter 2. Negation in logic and languageThe main aim of this book is to provide an account of the patterns of negation we find in natural language. The expression and interpretation of negation in natural language has long fascinated philosophers, logicians, and linguists. Horn's (1989) Natural history of negation opens with the following statement: "All human systems of communication contain a representation of negation. No animal communication system includes negative utterances, and consequently, none possesses a means for assigning truth value, for lying, for irony, or for coping with false or contradictory statements." A bit further on the first page, Horn states: "Despite the simplicity of the one-place connective of propositional logic (¬p is true if and only if p is not true) and of the laws of inference in which it participate (e.g. the Law of Double Negation: from ¬¬p infer p, and vice versa), the form and function of negative statements in ordinary Chapter 1 2 language are far from simple and transparent. In particular, the absolute symmetry definable between affirmative and negative propositions in logic is not reflected by a comparable symmetry in language structure and language use." The scope of this book is more modest than Horn's seminal study, but we will nevertheless attempt to work out some of the issues highlighted by Horn. In particular, we will be concerned with negation as a universal category of human language, with negation as the marked member of the pair , and with cross-linguistic variation in the marking and interpretation of propositional negation and negative indefinites. Markedness of negationThe fact that all human languages establish a distinction between affirmative and negative statements is the starting point of the investigation in Chapters 3 through 6.The relation with animal communication systems is investigated in Chapter 7, where we draw implications for language genesis from our study of negation in L2 acquisition. Modern studies on animal communication make it possible to assign a ment...

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“…In Zanuttini (1991), Haegeman and Zanuttini (1991) and ensuing work, this absorption is characterized as Neg-factorization, a rule of the syntax-semantics mapping which gets rid of the unwanted instances of logical negation under specified conditions. The alternative absorption rule in May (1989) involves the formation of a polyadic quantifier complex. Below I present a brief synopsis of Puskás's particular proposal.…”

Section: Are Hungarian N-words Negative?mentioning

confidence: 99%

“…See Surányi (2002c, Ch.5.2) for a feature valuation-based account. The account of de Swart and Sag (2002) treats this type of Negative Concord as a case of resumptive negative quantification within a polyadic quantifier approach, extending May's (1989) proposal. If it can be shown, as it will be in section 3 below, that n-words with a universal and an existential interpretation can coexist in the same clause, then a polyadic quantifier approach cannot cover Hungarian (only monadic quantifiers of the same type can merge into a polyadic quantifier).…”

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confidence: 99%

Quantification and focus in Negative Concord

Surányi

2006

Lingua

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Interpreting logical form

Cited by 83 publications

References 9 publications

Did Tarski commit “Tarski's fallacy”?

Did Tarski commit “Tarski's fallacy”?

Expression and Interpretation of Negation

Quantification and focus in Negative Concord

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