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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 ..."
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Cited by 163 (55 self)
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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...
Computing Ramifications by Postprocessing
 Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI
, 1995
"... A solution to the ramification problem caused by underlying domain constraints in Stripslike approaches is presented. We introduce the notion of causal relationships which are used in a postprocessing step after having applied an action description. Moreover, we show how the information needed for ..."
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Cited by 45 (3 self)
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A solution to the ramification problem caused by underlying domain constraints in Stripslike approaches is presented. We introduce the notion of causal relationships which are used in a postprocessing step after having applied an action description. Moreover, we show how the information needed for these postcomputations can be automatically extracted from the domain constraints plus general knowledge of which fluents can possibly affect each other. We illustrate the necessity of causal relationships by an example that shows the limitedness of a common method to avoid unintended ramifications, namely, the distinction between socalled frame and nonframe fluents. Finally, we integrate our solution into a recently developed, Stripslike yet purely deductive approach to reasoning about actions based on Equational Logic Programming. 1 Introduction The ramification problem [ Finger, 1987 ] is usually regarded as one of the challenges to all formal frameworks for reasoning about actions a...
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 ..."
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Cited by 35 (28 self)
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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
Let's Plan It Deductively
 Artificial Intelligence
, 1997
"... The paper describes a transition logic, TL, and a deductive formalism for it. It shows how various important aspects (such as ramification, qualification, specificity, simultaneity, indeterminism etc.) involved in planning (or in reasoning about action and causality for that matter) can be modell ..."
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Cited by 29 (0 self)
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The paper describes a transition logic, TL, and a deductive formalism for it. It shows how various important aspects (such as ramification, qualification, specificity, simultaneity, indeterminism etc.) involved in planning (or in reasoning about action and causality for that matter) can be modelled in TL in a rather natural way. (The deductive formalism for) TL extends the linear connection method proposed earlier by the author by embedding the latter into classical logic, so that classical and resourcesensitive reasoning coexist within TL. The attraction of a logical and deductive approach to planning is emphasized and the state of automated deduction briefly described. 1 Introduction Artificial Intelligence (AI, or Intellectics [Bib92a]) aims at creating artificial (or computational [PMG98]) intelligence. Were there no natural intelligence, the sentence would be meaningless to us. Hence understanding natural intelligence by necessity has always been among the goals of Intel...
On Proof Normalization in Linear Logic
 THEORETICAL COMPUTER SCIENCE
, 1994
"... We present a prooftheoretic foundation for automated deduction in linear logic. At first, we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a ..."
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Cited by 26 (12 self)
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We present a prooftheoretic foundation for automated deduction in linear logic. At first, we systematically study the permutability properties of the inference rules in this logical framework and exploit these to introduce an appropriate notion of forward and backward movement of an inference in a proof. Then we discuss the naturallyarising question of the redundancy reduction and investigate the possibilities of proof normalization which depend on the proof search strategy and the fragment we consider. Thus, we can define the concept of normal proof that might be the basis of works about automatic proof construction and design of logic programming languages based on linear logic.
A Resource Logic for MultiAgent Plan Merging
 Annals of Mathematics and Artificial Intelligence, special issue on Computational Logic on MultiAgent Systems
, 2003
"... In a multiagent system, agents are carrying out certain tasks by executing plans. Consequently, the problem of finding a plan, given a certain goal, has been given a lot of attention in the literature. Instead of concentrating on this problem, the focus of this paper is on cooperation between agent ..."
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Cited by 25 (10 self)
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In a multiagent system, agents are carrying out certain tasks by executing plans. Consequently, the problem of finding a plan, given a certain goal, has been given a lot of attention in the literature. Instead of concentrating on this problem, the focus of this paper is on cooperation between agents which already have constructed plans for their goals. By cooperating, agents might reduce the number of actions they have to perform in order to fulfill their goals. The key idea is that in carrying out a plan an agent possibly produces side products that can be used as resources by other agents. As a result, an other agent can discard some of its planned actions. This process of exchanging products, called plan merging, results in distributed plans in which agents become dependent on each other, but are able to attain their goals more efficiently.
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 ..."
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Cited by 24 (12 self)
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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 ...
A Relevant Analysis of Natural Deduction
 Journal of Logic and Computation
, 1999
"... Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and ..."
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Cited by 24 (7 self)
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Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lLcalculus; the representation mechanism is judgementsastypes, developed for relevant logics. The lLcalculus type theory is a firstorder dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required prooftheoretic metatheory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I calculus and ML with references. We describe the CurryHowardde Bruijn correspondence of the lLcalculus with a s...
linTAP: A Tableau Prover for Linear Logic
 International Conference TABLEAUX’99
, 1999
"... linTAP is a tableau prover for the multiplicative and exponential fragment M?LL of Girards linear logic. It proves the validity of a given formula by constructing an analytic tableau and ensures the linear validity using prex unication. We present the tableau calculus used by linTAP, an algorithm fo ..."
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Cited by 17 (6 self)
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linTAP is a tableau prover for the multiplicative and exponential fragment M?LL of Girards linear logic. It proves the validity of a given formula by constructing an analytic tableau and ensures the linear validity using prex unication. We present the tableau calculus used by linTAP, an algorithm for prex unication in linear logic, the linTAP implementation, and some experimental results obtained with linTAP. 1
Linear deductive planning
 JOURNAL OF LOGIC AND COMPUTATION
, 1996
"... Recently, three approaches to deductive planning were developed, which solve the technical frame problem without the need to state frame axioms explicitly. These approaches are based on the linear connection method, an equational Horn logic, and linear logic. At first glance these approaches seem to ..."
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Cited by 13 (1 self)
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Recently, three approaches to deductive planning were developed, which solve the technical frame problem without the need to state frame axioms explicitly. These approaches are based on the linear connection method, an equational Horn logic, and linear logic. At first glance these approaches seem to be very different. In the linear connection method a syntactical condition  each literal is connected at most once  is imposed on proofs. In the equational logic approach situations and plans are represented as terms and SLDEresolution is applied as an inference rule. The linear logic approach is a Gentzen style proof system without weakening and contraction rules. On second glance, however, and as a consequence of the results rigourously proved in this paper, it will turn out that the three approaches are equivalent. They are based on the very same idea that facts about a situation are taken as resources which can be consumed and produced.