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Firstorder Lax Logic as a Framework for Constraint Logic Programming
, 1997
"... In this report we introduce a new prooftheoretic approach to the semantics of Constraint Logic Programming, based on an intuitionistic firstorder modal logic, called QLL. The distinguishing feature of this new approach is that the logic calculus of QLL is used not only to capture the usual exte ..."
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Cited by 12 (4 self)
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In this report we introduce a new prooftheoretic approach to the semantics of Constraint Logic Programming, based on an intuitionistic firstorder modal logic, called QLL. The distinguishing feature of this new approach is that the logic calculus of QLL is used not only to capture the usual extensional aspects of Logic Programming, i.e. "which queries are successful, " but also some of the intensional aspects, i.e. "what is the answer constraint and how is it constructed." It provides for a direct link between the modeltheoretic and the operational semantics following a formulasasprograms and proofsasconstraints principle. This approach makes use of logic in a different way than other approaches based on logic calculi. On the one side it is to be distinguished from the wellknown provability semantics which is concerned merely with what is derivable as opposed to how it is derivable, paying attention to the fact that it is the how that determines the answer constraint. ...
Ternary Simulation: A Refinement of Binary Functions or an Abstraction of RealTime Behaviour?
 PROCEEDINGS OF THE 3RD WORKSHOP ON DESIGNING CORRECT CIRCUITS (DCC96
, 1996
"... We prove the equivalence between the ternary circuit model and a notion of intuitionistic stabilization bounds. The results are obtained as an application of the timing interpretation of intuitionistic propositional logic presented in [12]. We show that if one takes an intensional view of the ternar ..."
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Cited by 10 (3 self)
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We prove the equivalence between the ternary circuit model and a notion of intuitionistic stabilization bounds. The results are obtained as an application of the timing interpretation of intuitionistic propositional logic presented in [12]. We show that if one takes an intensional view of the ternary model then the delays that have been abstracted away can be completely recovered. Our intensional soundness and completeness theorems imply that the extracted delays are both correct and exact; thus we have developed a framework which unifies ternary simulation and functional timing analysis. Our focus is on the combinational behaviour of gatelevel circuits with feedback.
Proof Search in Constructive Logics
 In Sets and proofs
, 1998
"... We present an overview of some sequent calculi organised not for "theoremproving" but for proof search, where the proofs themselves (and the avoidance of known proofs on backtracking) are objects of interest. The main calculus discussed is that of Herbelin [1994] for intuitionistic lo ..."
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Cited by 9 (2 self)
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We present an overview of some sequent calculi organised not for "theoremproving" but for proof search, where the proofs themselves (and the avoidance of known proofs on backtracking) are objects of interest. The main calculus discussed is that of Herbelin [1994] for intuitionistic logic, which extends methods used in hereditary Harrop logic programming; we give a brief discussion of some similar calculi for other logics. We also point to some related work on permutations in intuitionistic Gentzen sequent calculi that clarifies the relationship between such calculi and natural deduction. 1 Introduction It is widely held that ordinary logic programming is based on classical logic, with a Tarskistyle semantics (answering questions "What judgments are provable?") rather than a Heytingstyle semantics (answering questions like "What are the proofs, if any, of each judgment?"). If one adopts the latter style (equivalently, the BHK interpretation: see [35] for details) by regardi...
Ternary Simulation: Refinement of Binary Functions
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©Copyright in this paper belongs to the author(s) Published in collaboration with the
Preface
"... These Lecture Notes describe the approach to the constructive analysis of computation as developed by Pierangelo Miglioli and his school. This Lecture Notes have been produced as the supporting material for the course in the Application of constructive logics to program analysis, synthesis and verif ..."
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These Lecture Notes describe the approach to the constructive analysis of computation as developed by Pierangelo Miglioli and his school. This Lecture Notes have been produced as the supporting material for the course in the Application of constructive logics to program analysis, synthesis and verification held in November 2006 at the Mathematisches
Abstraction and Constraints: Two Sides of the Same Coin
, 1997
"... ion and Constraints: Two Sides of the Same Coin M.Walton November 1997 University of Sheffield Department of Computer Science Technical Report CS9718 Abstraction and Constraints: Two Sides of the Same Coin M. Walton PhD Supervisor: M.V.H. Fairtlough Abstract This report presents a highlev ..."
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ion and Constraints: Two Sides of the Same Coin M.Walton November 1997 University of Sheffield Department of Computer Science Technical Report CS9718 Abstraction and Constraints: Two Sides of the Same Coin M. Walton PhD Supervisor: M.V.H. Fairtlough Abstract This report presents a highlevel survey of some approaches to abstraction and the wide range of fields in which their applications may be found. Whilst there is much to be found in the literature about either abstraction or constraints, very little is to be found about them both, or the relationship between them. We examine the role of a novel intuitionistic modal logic (called Lax Logic) in capturing the dual notions of abstraction and constraints, and a particular notion of refinement. As a specific application of Lax Logic, we look at its use as an abstraction framework for the paradigm of Constraint Logic Programming. This provides a novel declarative and operational semantics for CLP which offers a clean separation...