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Specification and Proof in Membership Equational Logic
 THEORETICAL COMPUTER SCIENCE
, 1996
"... This paper is part of a longterm effort to increase expressiveness of algebraic specification languages while at the same time having a simple semantic basis on which efficient execution by rewriting and powerful theoremproving tools can be based. In particular, our rewriting techniques provide s ..."
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Cited by 129 (52 self)
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semantic foundations for Maude's functional sublanguage, where they have been efficiently implemented. Membership equational logic is quite simple, and yet quite powerful. Its atomic formulae are equations and sort membership assertions, and its sentences are Horn clauses. It extends in a conservative
ON THE MATHEMATICAL SYNTHESIS OF EQUATIONAL LOGICS
"... Birkhoff [1935] initiated the general study of algebraic structure. Importantly for our concerns here, his development was from (universal) algebra to (equational) logic. Birkhoff’s starting point was the informal conception of algebra based on familiar concrete examples. Abstracting from these, he ..."
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Birkhoff [1935] initiated the general study of algebraic structure. Importantly for our concerns here, his development was from (universal) algebra to (equational) logic. Birkhoff’s starting point was the informal conception of algebra based on familiar concrete examples. Abstracting from these, he
Local Equational Logic II
"... A logic may be called local if each model may be used to define the truth. In the proposition calculus each boolean algebra define the truth by its greatest element. In the equational logic the equality between the algebra elements define the truth. In the clause Horn logic the truth is given by the ..."
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A logic may be called local if each model may be used to define the truth. In the proposition calculus each boolean algebra define the truth by its greatest element. In the equational logic the equality between the algebra elements define the truth. In the clause Horn logic the truth is given
Equational logic and theories of action
 PROCEEDINGS OF THE APPIAGULPPRODE JOINT CONFERENCE ON DECLARATIVE PROGRAMMING
, 1996
"... This is a survey on reasoning about situations, actions, and causality within equational logic. Its main feature is the representation of situations as multisets of resources. Such resources are consumed whenever the conditions of an action are satisfied and are produced whenever the action is appli ..."
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Cited by 1 (1 self)
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This is a survey on reasoning about situations, actions, and causality within equational logic. Its main feature is the representation of situations as multisets of resources. Such resources are consumed whenever the conditions of an action are satisfied and are produced whenever the action
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
On Extra Variables in (Equational) Logic Programming
, 1994
"... Extra variables in a clause are variables which occur in the body but not in the head. It has been argued that extra variables are necessary and contribute to the expressive power of logic languages. In the first part of this paper, we show that this is not true in general. For this purpose, we p ..."
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Cited by 23 (2 self)
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use a similar technique to provide new completeness results for equational logic programs with extra variables. In equational logic programming it is well known that extra variables cause problems since narrowing, the standard operational semantics for equational logic programming, may become
Equational Logic of Polynomial Coalgebras
, 2001
"... Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and statetransition systems. This paper presents a calculus of terms for operations on such coalgebras, based on a simple type theory, and develops its ..."
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Cited by 7 (2 self)
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Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and statetransition systems. This paper presents a calculus of terms for operations on such coalgebras, based on a simple type theory, and develops its semantics. The terms admit a single statevalued parameter, but may also have statevalued variables. In a "rigid" term all statevariables are bound. Boolean
Completeness of manysorted equational logic
 Houston Journal of Mathematics
, 1985
"... ABSTRACT. Assuming that manysorted oquationallogic "goes just as for the onesorted case " has led to incorrect statements of results in manysorted universal algebra; in fact, the onesorted rules are not sound for manysortededuction. This paper gives sound and complete rules, and chara ..."
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Cited by 71 (7 self)
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; by Lawvere and Benabou); this allows a full algebraization of manysorted equational deduction that is not possible with the usual fully invariant congruences on the free algebra on countably many generators. 1. Introduction. The
Results 1  10
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