In his development of formal semantics for natural language Montague [1970a]– Montague [1973], 1 Richard Montague modeled the meaning (Frege’s sense) of a term A by its Carnap intension CI(A), the function which assigns to each state a, specifying a “possible world”, “time ” and “context of use”, the denotation den(A)(a) of A in that state. Now this is surely not right: among other things, it makes “there are infinitely many odd numbers ” synonymous with “there are infinitely many prime numbers”, which it is not. 2 At the other extreme, “structural ” approaches to the modeling of meaning (like Russell’s propositions, 3 Church [1946]–Church [1974] and Cresswell [1985]) basically tell us no more than that “the sense of a complex term A can be determined from the syntactic structure of A and the senses or denotations of the basic constituent parts of A”, without explaining how this “determination ” is to take place. But, to oversimplify Davidson’s eloquent criticism in Davidson [1967], Theaetetus and the property of flying do not (by themselves) amount to the meaning of “Theaetetus flies”: we would like to know just what kind of objects meanings are, and how the meaning of “Theaetetus flies ” is determined by the meanings of

This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an object-oriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have

this paper, and for their invaluable corrections and comments to earlier drafts

The signature and logical calculus of the algebraic specification language Spectrum are formalized in the generic language Deva. This language is designed to express formal methods as well as proofs of propositions about the objects of such methods and the relations between them. This work

The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed -calculus with dependent types. Syntax is treated in a style similar to, but more general than, Martin-Lof's system

A logical calculus, not unlike Gentzen's sequent calculus for intuitionist logic, is described which is sound for polynomial-time realizability as defined by Crossley and Remmel. The sequent calculus admits cut elimination, thus giving a decision procedure for the propositional fragment. 0

, encapsulation, and others. In a sense, F-logic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. F-logic has a model-theoretic semantics and a sound and complete resolution-based proof theory. A small number of fundamental concepts

This paper proposes a new logic programming language called GOLOG whose interpreter automatically maintains an explicit representation of the dynamic world being modeled, on the basis of user supplied axioms about the preconditions and effects of actions and the initial state of the world

that Dedekind cuts and Cauchy sequences fail to join in algebraical operations and thus lack intuition; third, we construct a logical calculus and deduce numbers to intuitively and logically denote number systems. 1.

Abstract. We present a resolution based reasoning algorithm called DL calculus that decides concept satisfiability for the SHIQ language. Unlike existing resolution based approaches, the DL calculus is defined directly on DL expressions. We argue that working on this high level of abstraction