In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

This volume presents significant developments in the field of Montague Grammar and outlines its past and future contributions to philosophy and linguistics. The contents are as follows: Introduction by Steven Davis and Marianne Mithun Emmon Bach, "Montague Grammar and Classical Transformational Grammar" Barbara H. Partee, "Constraining Transformational Montague Grammar: A Framework and a Fragment" James D. McCawley, "Helpful Hints to the Ordinary Working Montague Grammarian" Terence Parsons, "Type Theory and Ordinary Language" David (...) R. Dowty, "Dative 'Movement' and Thomason's Extensions of Montague Grammar" Muffy E. A. Siegel, "Measure Adjectives in Montague Grammar" Michael Bennett, "Mass Nouns and Mass Terms in Montague Grammar" Jeroen Groenendijk and Martin Stokhof, "Infinitives and Context in Montague Grammar" James Waldo, "A PTQ Semantics for Sortal Incorrectness". (shrink)

We started from the fact that type theory, in the way it was implemented in IL, makes it costly to deal with nominalization processes. We have also argued that the type hierarchy as such doesn't play any real role in a grammar; the classification it provides for different semantic objects is already contained, in some sense, in the categorial structure of the grammar itself. So, on the basis of a theory of properties (Cocchiarella's HST*) we have tried to (...) build a language (IL*) whose syntax does not contain any explicit typing of expressions. Some of the consequences that this move brings about in the overall organization of the grammar can be summarized as follows:it allows for a simple treatment of infinitives, gerunds, factives and, in general, all those phenomena which might be analyzed as cases of nominalization;it provides a simpler and more constrained semantics than IL, since IL* doesn't go beyond second order, and its non-modal basis is axiomatizable;it suggests that the role of logical form in a theory of grammar could be that of a family of theories of semantic objects;it eliminates the extrinsic limitations of a type hierarchy on the choice of the system of syntactic categories.I think that it is interesting to notice how having an explicit semantic framework helps to provide a sense in which it is legitimate to regard the syntax of a language as ‘autonomous’. (shrink)

This is what I hope is an illuminating, and to a certain degree, novel exposition of Montague Grammar. It is against many standard interpretations, and perhaps even against things Montague himself says at times. However, it makes more sense of how his various commitments fit together in a systematic way. Why, for instance, is it called "Montague Grammar" rather than "Montague Semantics," and what role does his commitment to Fregeanism plays in his conception of (...) language? It is clear that he is committed to the idea that function application is the fundamental mode of semantic composition, and that he is committed to an intensional framework. However, intensions have, since Carnap, been understood as nearly conceptually equivalent to functions from possible worlds to sets of individuals. But, in truth, possible worlds semantics is just dressed up extensional semantics. There are just more objects to go around to serve as inputs for functions, whatever we think of their ontological status. That is, possible worlds semantics is really a semantic reduction of intensional semantics achieved by expanding our ontological commitments. It would be difficult to make sense of Montague's strong commitment to Fregean semantics, if his notion of intension was that of Carnap's. According to my interpretation, Montague's notion of intension must be distinct from the version adopted by possible world semantics. Montague took seriously the idea that intensional semantics was something quite different from extensionalist semantics. The first was not reducible to the second semantically speaking. Just as Frege believed that meaning consisted of both sense and reference, so too did Montague. However, just as Frege also believed, Montague thought that sense and reference were systematically related. As I illustrate, interpreting Montague as adopting a different notion of intension can also resolve the apparent problem of distinguishing the difference in meaning between intensional equivalents. It might also enable us to draw a distinction in epistemic logic between an agent having contradictory beliefs and believing contradictions. (shrink)

The main result in this paper is a method for obtaining derivation trees from sentences of certain formal grammars. No parsing algorithm was previously known to exist for these grammars.Applied to Montague's PTQ the method produces all parses that could correspond to different meanings. The technique directly addresses scope and reference and provides a framework for examining these phenomena. The solution for PTQ is implemented in an efficient and useful computer program.

INTRODUCTION Linguists who work within the tradition of transformational generative grammar tend to regard semantics as an intractable, perhaps ultimately ...

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, (...) fstructures) are somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure. (shrink)

Introduction -- 1. The settling of a language -- 2. The Whorf hypothesis -- 3. Relativism or a universal theory? -- 4. What does language have to do with logic and mathematics? -- 5. A test bed for grammatical theories -- 6. The Chomsky hierarchy in perpsective -- 7. Reflexivity and identity in language and cognition -- 8. The generalized logic hierarchy and its cognitive implications -- 9. The intensionalization of extensions.

In this small book logician and mathematician Jens Erik Fenstad addresses some of the most important foundational questions of linguistics: What should a theory of meaning look like and how might we provide the missing link between meaning theory and our knowledge of how the brain works? The author’s answer is twofold. On the one hand, he suggests that logical semantics in the Montague tradition and other broadly conceived symbolic approaches do not suffice. On the other hand, he does (...) not argue that the logical approach should be discarded; instead, he opts for a methodological pluralism in which symbolic approaches to meaning are combined with geo- metric ones such as Conceptual Spaces [9] and discusses ways in which these geometric accounts could be hooked up with connectionist frameworks and dynamic systems approaches in neurophysiology. (shrink)

My point in this paper is to focus on some details of Alfred Tarski’s writing that in my opinion have not been aptly represented — or aptly rejected — in Richard Montague’s grammar and to agree with those who share Tarski’s view that human language is something uncapturable. The paper consists of two parts, concerning 1) some attempts to formalize the non-declarative utterances, and 2) the limitations of T-scheme and of Montague grammar.

Abstract -/- Quantifier domain restriction (QDR) and two versions of nominal restriction (NR) are implemented as restrictions that depend on a previously introduced interpreter and interpretation time in a two-dimensional semantic framework on the basis of simple type theory and categorial grammar. Against Stanley (2002) it is argued that a suitable version of QDR can deal with superlatives like tallest. However, it is shown that NR is needed to account for utterances when the speaker intends to convey different restrictions (...) for multiple uses of the same quantifying determiner. We argue that NR generally fares better with such examples but also observe that examples like Every sailor waves at every sailor might be pragmatically anomalous. An account of contextual domain restriction is proposed that (i) excludes these anomalous readings (but it is shown how they could be included), (ii) makes it possible to express different contextual domain restrictions as long-range dependencies on an interpreter and an interpretation time, and (iii) additionally models restrictions based on locative constructions as general mereological constraints introduced by shifting the index. (shrink)

Sound and Grammar: A Neo-Sapirian Theory of Language by Susan F. Schmerling offers an original overall linguistic theory based on the work of the early American linguist Edward Sapir, supplemented with ideas from the philosopher-logicians Kazimierz Ajdukiewicz and Richard Montague and the linguist Elisabeth Selkirk. The theory yields an improved understanding of interactions among different aspects of linguistic structure, resolving notorious issues directly inherited by current theory from (post- ) Bloomfieldian linguistics. In the theory presented here, syntax is (...) a filter on a phonological algebra, not a linguistic level; linguistic expressions are phonological structures, and syntax is semantically relevant relations among phonological structures. The book shows how Neo-Sapirian grammar sheds new light on syntax-phonology interactions in English, German, French, and Spanish. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was (...) taken to be that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

In this paper we show that the membership problem for second order non-linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own.

Franz Brentano’s theory of emotion is tightly bound up with many of his other central claims, in such a way that one has to work out how it relates to these other claims if one is to understand its distinctive character. There are two main axes of investigation. The first results from the fact that Brentano introduces his theory of emotion as part of his overall theory of mind, which consists of a number of closely interconnected theses concerning the nature (...) of mental phenomena, the nature of consciousness, and the classification of mental phenomena into fundamental kinds (Brentano 1874/1973a). The second derives from the fact that his theory of emotion also forms the foundation of his epistemology of objective value, which he elaborates in a framework constituted by an epistemic theory of truth and an extended analogy he draws between emotions and judgments (Brentano 1889/1969). I will consider both of these axes in what follows. (shrink)

Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...) They propose instead that the semantic values of sentences must be structured propositions. In rejecting intensional semantics, philosophers who endorse structured propositions also usually reject functional compositionality, undermining both tenets of the Montagovian programme. I defend a semantic theory that incorporates both structured propositions and functional compositionality. I argue that this semantic theory can preserve many explanatory benefits of Montague semantics. Finally, I show how treating composition functional application can resolve core problems internal to a theory of structured propositions. (shrink)

This concise introduction examines a wide range of ethical positions, including relativism, emotivism, egoism, utilitarianism, Kantian formalism, & natural law.

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis, is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken (...) to be that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

In this paper, we shall present a generalization of phrase structure grammar, in which all functional categories have type restrictions, that is, their argument types are specific domains. In ordinary phrase structure grammar, there is just one universal domain of individuals. The grammar does not make a distinction between verbs and adjectives in terms of domains of applicability. Consequently, it fails to distinguish between sentences like every line intersects every line, which is well typed, and every line (...) intersects every point, which is ill typed.Our generalization relates to ordinary phrase structure grammar in the same way as the higherlevel constructive type theory of Martin-Löf relates to the simple type theory of Church . Simple type theory has been used in linguistics and related with phrase structure grammar, especially in the tradition based on the work of Montague .Our definition of the grammar will be more formal than Montague's in the sense that we shall use a formal metalanguage, that of constructive type theory, for defining both the object language and its interpretation. The grammar, both syntax and semantics, is thus readily implementable in the type-theoretical proof system ALF . Inside type theory, a distinction can be made between the object language and the model, in other words, between syntactic and semantic types. It will turn out that the object language cannot be defined independently of the model, as in ordinary Tarski semantics. This is a direct consequence of introducing the typing restrictions.The grammar presented here can be seen as a formal linguistic elaboration of the work presented in Ranta 1991 and 1994. The organization of generative grammar as categorial grammar followed by sugaring should now look more familiar to the linguist, as the grammatical formalism on which sugaring operates is no longer full type theory but a set of phrase structure trees. (shrink)

Does thought have distinctive experiential features? Is there, in addition to sensory phenomenology, a kind of cognitive phenomenology--phenomenology of a cognitive or conceptual character? Leading philosophers of mind debate whether conscious thought has cognitive phenomenology and whether it is part of conscious perception and conscious emotion.

This paper focuses on Aquinas’s doctrine of individuation as it applies to human beings. There are three main sections. In the first, the general lines of Aquinas’s doctrine of individuation are presented in the context of discussing an article by Joseph Owens and some other recent work on individuation. I argue for form as the primary principle of individuation and specify the uniqueness of human individuality by reference to the degrees of perfection among things. The second section focuses on three (...) ways in which a meditation on our form—the rational soul—is fruitful for understanding what makes us individuals. Here I consider, in turn, the three distinctive activities of human reason—theoretical, moral, and aesthetic. Each activity is presented as it relates to three levels of perfection in the human being. In the third section, I bring up three pertinent objections to my thesis and suggest answers to them. (shrink)

In American philosophy at the end of the nineteenth century there was small interest in Empiricism and almost no interest in Realism.