Results 1  10
of
19
Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
Abstract

Cited by 169 (57 self)
 Add to MetaCart
Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
Abstract

Cited by 42 (3 self)
 Add to MetaCart
This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
Computing Change and Specificity with Equational Logic Programs
"... this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specificity is computed with the help of negation ..."
Abstract

Cited by 35 (28 self)
 Add to MetaCart
this paper, we present an equational logic framework for objects, methods, inheritance and overriding of methods. Overriding is achieved via the concept of specificity, which states that more specific methods are preferred to less specific ones. Specificity is computed with the help of negation as failure. We specify equational logic programs and show that their completed versions behave as intended. Furthermore, we prove that SLDENFresolution is complete if the equational theory is finitary, the completed programs are consistent, and no derivation flounders or is infinite; and we give syntactic conditions which guarantee nonfloundering and finiteness. Finally, we discuss how the approach can be extended to reasoning about the past in the context of incompletely specified objects or situations. It will turn out that constructive negation is needed to solve these problems
Representing Actions in Equational Logic Programming
 Proceedings of the International Conference on Logic Programming (ICLP
, 1994
"... A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resourceoriented equational logic based approach and various other methods designed for reasoning a ..."
Abstract

Cited by 24 (12 self)
 Add to MetaCart
(Show Context)
A sound and complete approach for encoding the action description language A developed by M. Gelfond and V. Lifschitz in an equational logic program is given. Our results allow the comparison of the resourceoriented equational logic based approach and various other methods designed for reasoning about actions, most of them based on variants of the situation calculus, which were also related to the action description language recently. A nontrivial extension of A is proposed which allows to handle uncertainty in form of nondeterministic action descriptions, i.e. where actions may have alternative randomized effects. It is described how the equational logic programming approach forms a sound and complete encoding of this extended action description language AND as well. 1 Introduction Understanding and modelling the ability of humans to reason about actions, change, and causality is one of the key issues in Artificial Intelligence and Cognitive Science. Since logic appears to play ...
Actions and Specificity
 Proceedings of the International Logic Programming Symposium (ILPS
, 1993
"... A solution to the problem of specificity in a resourceoriented deductive approach to actions and change is presented. Specificity originates in the problem of overloading methods in object oriented frameworks but can be observed in general applications of actions and change in logic. We give a unif ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
(Show Context)
A solution to the problem of specificity in a resourceoriented deductive approach to actions and change is presented. Specificity originates in the problem of overloading methods in object oriented frameworks but can be observed in general applications of actions and change in logic. We give a uniform solution to the problem of specificity culminating in a completed equational logic program with an equational theory. We show the soundness and completeness of SLDENFresolution, ie. SLDresolution augmented by negationasfailure and by an equational theory, wrt. the completed program. Finally, the expressiveness of our approach for performing general reasoning about actions, change, and causality is demonstrated.
Action and Change in Rewriting Logic
, 1996
"... Rewriting logic is proposed as a logic of concurrent action and change that solves the frame problem and that subsumes and unifies a number of previous logics of change, including linear logic and Horn logic with equality. Rewriting logic can represent action and change with great flexibility and ge ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
Rewriting logic is proposed as a logic of concurrent action and change that solves the frame problem and that subsumes and unifies a number of previous logics of change, including linear logic and Horn logic with equality. Rewriting logic can represent action and change with great flexibility and generality; this flexibility is illustrated by many examples, including examples that show how concurrent objectoriented systems are naturally represented. In addition, rewriting logic has a simple formalism, with only a few rules of deduction; it supports userdefinable logical connectives, which can be chosen to fit the problem at hand; it is intrinsically concurrent; and it is realizable in a wide spectrum logical language (Maude and its MaudeLog extension) supporting executable specification and programming. Contents 1 Introduction 2 1.1 What the frame problem (in our sense) is . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 What the frame problem (in our sense) is not . . . . . . ....
Solving Deductive Planning Problems Using Program Analysis and Transformation
, 1995
"... Two general, problematic aspects of deductive planning, namely, detecting unsolvable planning problems and solving a certain kind of postdiction problem, are investigated. The work is based on a resource oriented approach to reasoning about actions and change using a logic programming paradigm. We s ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Two general, problematic aspects of deductive planning, namely, detecting unsolvable planning problems and solving a certain kind of postdiction problem, are investigated. The work is based on a resource oriented approach to reasoning about actions and change using a logic programming paradigm. We show that ordinary resolution methods are insufficient for solving these problems and propose program analysis and transformation as a more promising and successful way to tackle them. In particular, a recently developed specialization technique based on partial evaluation and regular approximation is refined and adapted for the specialization of the underlying logic program modeling actions and change. Furthermore, a regular approximation is proposed as a finite description for representing and collecting infinitely many combinations of resources. The usefulness of the developed specialization techniques are demonstrated on some prototypical examples.
Descriptions in the Fluent Calculus
"... An attempt to combine reasoning about actions in the uent calculus with description logics is described. It extends description logics in that concepts may be situation{dependent. In particular, an object may belong to a dierent concept before and after the execution of an action. It extends the uen ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
An attempt to combine reasoning about actions in the uent calculus with description logics is described. It extends description logics in that concepts may be situation{dependent. In particular, an object may belong to a dierent concept before and after the execution of an action. It extends the uent calculus by inheritance and overriding of action descriptions and, in particular, it generalizes the work reported in [5]. Keywords: Knowledge Representation, Reasoning about Actions, Fluent Calculus, Description Logics, Specicity. 1 Introduction In almost all applications of logic based approaches to reasoning about actions the underlying domain is at and unstructured (see e.g. [7]). Concepts, hierarchies and taxonomies are usually not specied or used in the denition of actions. Inheritance does not play a role in many formalisms for reasoning about actions, although this is known to be a quite powerful technique. In particular  and this is a major drawback of current proposals...
Deductive Plan Generation
 Algorithmic Learning TheoryProc. AII and ALT, volume 872 of LNAL p. 25, Iteinhardsbrmm
, 1994
"... ..."
(Show Context)
The Event Calculus as a Linear Logic Program
, 1995
"... . The traditional presentation of Kowalski's Event Calculus as a logic program uses Negationas Failure (NAF) in an essential way to support persistence of fluents. In this paper we present an implementation of Event Calculus as a purely logical (without NAF) Linear Logic (LL) program. This wor ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. The traditional presentation of Kowalski's Event Calculus as a logic program uses Negationas Failure (NAF) in an essential way to support persistence of fluents. In this paper we present an implementation of Event Calculus as a purely logical (without NAF) Linear Logic (LL) program. This work demonstrates some of the internal nonmonotonic features of LL and its suitability for knowledge update (as opposed to knowledge revision). Although NAF is an ontologically sufficient solution to the frame problem, the LL solution is implementationally superior. Handling of incomplete temporal descriptions and support for ramifications (derived fluents) are also considered. Keywords: event calculus, linear logic, negation as failure, knowledge update. 1 Introduction The Event Calculus (EC) of [ Kowalski and Sergot, 1986 ] is a theory of events (actions) and the fluents (predicates) that they precipitate. An important property of the theory is that it is rendered as a logic program, and is thu...