It is the aim of INDICES to document recent explorations in the various fields of philosophical logic and formal linguistics and their applications in other disciplines. The main emphasis of this series is on self-contained monographs covering particular areas of recent research and surveys of methods, problems, and results in all fields of inquiry where recourse to logical analysis and logical methods has been fruitful. INDICES will contain monographs dealing with the central areas of philosophical logic (extensional and intensional systems, (...) indexical logics, non-classical logics, philosophy of logic, etc.) as well as studies in which these systems are applied to specific issues in philosophy, in the formal semantics of natural languages, the foundations of linguistic theory, in computational linguistics, and in theoretical computer science. Constructive type theory was first presented in 1970, by the Swedish logician Per Martin-Lof. It has become one of the main approaches used in the foundations of mathematics and computer science. But it has remained relatively unknown among linguists and philosophers, although it provides a considerable extension of the concepts and techniques of logic. The book first gives an introduction to type theory from the point of view of linguistics and the philosophy of language. Type theory is then applied in the areas of quantification, anaphora, temporal reference, and the structure of text and discourse. By virtue of the type-theoretical concepts of proof object and context, various phenomena of dependence and progression in language can be discussed in precise terms, and several well-known problems can be solved. A categorial grammar is presented togenerate formally a fragment of English, together with an example of a computer implementation. (shrink)

This extended investigation of the semantics of event (and state) sentences in their various forms is a major contribution to the semantics of natural language, simultaneously encompassing important issues in linguistics, philosophy, and logic. It develops the view that the logical forms of simple English sentences typically contain quantification over events or states and shows how this view can account for a wide variety of semantic phenomena. Focusing on the structure of meaning in English sentences at a &"subatomic&" level&-that is, (...) a level below the one most theories accept as basic or &"atomic&"&-Parsons asserts that the semantics of simple English sentences require logical forms somewhat more complex than is normally assumed in natural language semantics. His articulation of underlying event theory explains a wide variety of apparently diverse semantic characteristics of natural language, and his development of the theory shows the importance of seeing the distinction between events and states. Parsons demonstrates that verbs, also, indicate kinds of actions rather than specific, individual actions. Verb phrases, too, he argues, depend on modifiers to make their function and meaning in a sentence specific. An appendix gives many of the details needed to formalize the theory discussed in the body of the text and provides a series of templates that permit the generation of atomic formulas of English. (shrink)

Inertia is enshrined in Newton’s first law of motion, a body at rest or in uniform motion remains in that state unless a force is applied to it. Now, consider (1). (1) Pat stopped the car before it hit the tree. Can we conclude from (1) that the car struck the tree? Not without further information such as that supplied in (2). (2) But the bus behind kept going. A post-condition for Pat stopping the car is that the car be (...) at rest. To satisfy a pre-condition for the car hitting the tree (namely, that the car not be at rest), inertia requires that some intervening force act on the car (as hinted, for example, by (2)). In the absence of such a force, (1) would appear to suggest that Pat prevented a collision between car and tree. Exactly what bit of physics are we importing into natural language interpretation here? Oversimplified, Newton’s first law of motion says: no change without force. Identifying force with cause, we come to the slogan no temporality without cause, capturing in a phrase the proposal from Steedman 2000 that.. (shrink)

The “surge in use of finite-state methods” ([10]) in computational linguistics has largely, if not completely, left semantics untouched. The present paper is directed towards correcting this situation. Techniques explained in [1] are applied to a fragment of temporal semantics through an approach we call finite-state temporality. This proceeds from the intuition of an event as “a series of snapshots” ([15]; see also [12]), equating snapshots with symbols that collectively form our alphabet. A sequence of snapshots then becomes a string (...) over that alphabet, evoking comic/film strips. Jackendoff has, among others, objected to conceptualizing events in terms of snapshots ([8]). To counter these objections, we step up from events-as-strings to event-typesas-regular languages ([5, 6]), recognizing the need for variable granularity. Beyond the introduction of disjunction implicit in the step from a single string up to a set of strings, we obtain a useful logic from the regular operations and a careful choice of the snapshots (constituting our alphabet). (shrink)

I will explore possibilities for formulating linguistic semantics in terms of records and record types of the kind used in recent developments of Martin-L¨of type theory (Betarte, 1998, Betarte and Tasistro, 1998, Coquand, Pollock and Takeyama, 2003, Tasistro, 1997). I will suggest that they give us the tools to develop a theory which includes aspects of Montague semantics, using the lambda calculus1, Discourse Representation Theory (DRT)2, situation semantics3 and Head-Driven Phrase Structure Grammar (HPSG)4 in a single theory. I will also (...) argue that formulating these theories in terms of record types may provide us not only with a unified approach but also with certain improvements over the individual theories. (shrink)