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Reflection in membership equational logic, manysorted equational logic, horn logic with equality, and rewriting logic
 In Gadducci and Montanari [33
, 2002
"... We show that the generalized variant of rewriting logic where the underlying equational specifications are membership equational theories, and where the rules are conditional and can have equations, memberships and rewrites in the conditions is reflective. We also show that membership equational log ..."
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Cited by 20 (6 self)
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logic, manysorted equational logic, and Horn logic with equality are likewise reflective. These results provide logical foundations for reflective languages and tools based on these logics, and in particular for the Maude language itself. 1
Connecting ManySorted Theories’, The
 Journal of Symbolic Logic
, 2007
"... Abstract. Basically, the connection of two manysorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of ..."
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Cited by 24 (7 self)
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. The combination of decision procedures for logical theories arises in many areas of logic in computer science, such as constraint solving, automated deduction, term rewriting, modal logics, and description logics. In general, one has two firstorder theories T1 and T2 over signatures Σ1 and Σ2, for which
Membership Algebra as a Logical Framework for Equational Specification
, 1998
"... This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms ..."
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Cited by 176 (61 self)
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This paper proposes membership equational logica Horn logic in which the basic predicates are equations t = t 0 and membership assertions t : s stating that a term t belongs to a sort sas a logical framework in which a very wide range of total and partial equational specification formalisms
Term Rewriting Systems
, 1992
"... Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss Abstra ..."
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Cited by 613 (18 self)
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Term Rewriting Systems play an important role in various areas, such as abstract data type specifications, implementations of functional programming languages and automated deduction. In this chapter we introduce several of the basic comcepts and facts for TRS's. Specifically, we discuss
Constraint Logic Programming: A Survey
"... Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve in differe ..."
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Cited by 864 (25 self)
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Constraint Logic Programming (CLP) is a merger of two declarative paradigms: constraint solving and logic programming. Although a relatively new field, CLP has progressed in several quite different directions. In particular, the early fundamental concepts have been adapted to better serve
Maude: Specification and Programming in Rewriting Logic
, 2001
"... Maude is a highlevel language and a highperformance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and ..."
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Cited by 210 (66 self)
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and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object
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 ..."
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Cited by 131 (54 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
Parametric Shape Analysis via 3Valued Logic
, 2001
"... Shape Analysis concerns the problem of determining "shape invariants"... ..."
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Cited by 660 (79 self)
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Shape Analysis concerns the problem of determining "shape invariants"...
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 621 (72 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
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 169 (57 self)
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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
Results 1  10
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