Montague’s framework for semantic interpretation has always been less well adapted to the interpretation of words than of syntactic constructions. In the late 1970s, David Dowty addressed this problem, concentrating on the interpretation of tense, aspect, inchoatives, and causatives in an extension of Montague’s Intensional Logic. In this paper I will try to revive this project, conceiving it a...

Classical logical optimization techniques rely on a logical semantics of the query language. The adaptation of these techniques to XQuery is precluded by its definition as a functional language with operational semantics. We introduce Nested XML Tableaux which enable a logical foundation for XQuery semantics and provide the logical plan optimization framework of our XQuery processor. As a proof...

We present a semantics (using Kripke lambda models) for a logical framework (minimal implicational predicate logic with quantiication over all higher types). We apply the semantics to obtain straightforward adequacy proofs for encodings of logics in the framework.

We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphism map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multiparadigm languages, especially structuring specifications (module systems) á la OBJ-Cle...

This chapter introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other chapters in this volume consider approaches that attempt to reproduce aspects of logical semantics within new frameworks. The approach we present here is different: We show how logical semantics can be embedded within a vector space framework, and u...

Provably correct compilation is an important aspect in development of high assurance software systems. In this paper we present an approach to provably correct compilation based on Horn logical semantics of programming languages and partial evaluation. We also show that continuation semantics can be expressed in the Horn logical framework, and introduce Definite Clause Semantics. We illustrate ...

Provably correct compilation is an important aspect in development of high assurance software systems. In this paper we explore approaches to provably correct code generation based on programming language semantics, particularly Horn logical semantics, and partial evaluation. We show that the definite clause grammar (DCG) notation can be used for specifying both the syntax and semantics of impe...

We continue with the task of obtaining a unifying view of process semantics by considering in this case the logical characterization of the semantics. We start by considering the classic linear timebranching time spectrum developed by R.J. van Glabbeek. He provided a logical characterization of most of the semantics in his spectrum but, without following a unique pattern. In this paper, we pres...

We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of generative probabilistic systems. We provide a sufficient condition under which a logical semantics coincides with the trace semantics obtained via a given determin...

The abstract interpretation of programs relates the exact semantics of a programming language to a finite approximation of those semantics. In this article, we describe an approach to abstract interpretation that is based in logic and logic programming. Our approach consists of faithfully representing a transition system within logic and then manipulating this initial specification to create a ...