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A LOGICAL CALCULUS OF MEANING AND SYNONYMY
"... 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”, th ..."
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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
A Linear Logic Calculus of Objects
 Proceedings of the Joint International Conference and Symposium on Logic Programming
, 1996
"... This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an objectoriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have rec ..."
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Cited by 10 (5 self)
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This paper presents a linear logic programming language, called O \Gammaffi , that gives a complete account of an objectoriented calculus with inheritance and override. This language is best understood as a logical counterpart the object and record extensions of functional programming that have
A Logical Calculus Of Meaning And Synonymy
, 2003
"... this paper, and for their invaluable corrections and comments to earlier drafts ..."
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this paper, and for their invaluable corrections and comments to earlier drafts
Formalization of the SPECTRUM Methodology in DEVA: Signature and Logical Calculus
, 1993
"... 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 is under ..."
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Cited by 5 (1 self)
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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
A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... 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, MartinLof's system of ariti ..."
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Cited by 795 (42 self)
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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, MartinLof's system
A Logical Calculus for Polynomialtime Realizability
 Journal of Methods of Logic in Computer Science
, 1991
"... A logical calculus, not unlike Gentzen's sequent calculus for intuitionist logic, is described which is sound for polynomialtime realizability as defined by Crossley and Remmel. The sequent calculus admits cut elimination, thus giving a decision procedure for the propositional fragment. 0 Intr ..."
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Cited by 3 (0 self)
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A logical calculus, not unlike Gentzen's sequent calculus for intuitionist logic, is described which is sound for polynomialtime realizability as defined by Crossley and Remmel. The sequent calculus admits cut elimination, thus giving a decision procedure for the propositional fragment. 0
Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 876 (65 self)
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, encapsulation, and others. In a sense, Flogic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. Flogic has a modeltheoretic semantics and a sound and complete resolutionbased proof theory. A small number of fundamental concepts
GOLOG: A Logic Programming Language for Dynamic Domains
, 1994
"... 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. This allo ..."
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Cited by 628 (74 self)
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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
A LOGICAL CALCULUS TO INTUITIVELY AND LOGICALLY DENOTE NUMBER SYSTEMS
, 805
"... Abstract. Simple continued fractions, baseb expansions, Dedekind cuts and Cauchy sequences are common notations for number systems. In this note, first, it is proven that both simple continued fractions and baseb expansions fail to denote real numbers and thus lack logic; second, it is shown that ..."
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Cited by 2 (1 self)
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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.
A Resolution Based Description Logic Calculus
"... 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 provid ..."
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Cited by 3 (2 self)
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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
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