Razvan Diaconescu. Completeness of semantic paramodulation: a category-based approach. International Journal of Foundations of Computer Science. To appear.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in our very broad sense. Rewriting is defined on algebraic entities more abstract than terms by abstracting the properties of contexts from the standard cases, and paramodulation is generalised to semantic paramodulation, defined by an inference rule over an arbitrary fixed model (see [13] or [11] for the CB approach to semantic paramodulation) This contrasts with the usual combinatorial paramodulation based operational approaches. This semantic perspective motivates paramodulation modulo a model morphism, which we use to show that computing in the quotient model of a theory is the same ....

Razvan Diaconescu. Completeness of semantic paramodulation: a category-based approach. International Journal of Foundations of Computer Science. To appear.

....subcategory of MOD(S(T ) satisfying the theory T . Lemma 3.1. If the institution is liberal and the category of models of each signature has J colimits, then MOD(T ) has J colimits for each theory T . 7 When regarded as theory morphisms between the corresponding empty theories. R azvan Diaconescu 10 Proof. Let A : J MOD(T ) be a J diagram of T models. Let be the colimit of this diagram in MOD(S) where S is the signature of T (also let i denote the inclusion S T ) A i a i ## A u ## i ## # # # # # # # # # # # # C Colim(A;MOD(i) f ## # # # # # # # # # # # # f ## # # # # # # ....

....a category Sys S . The category of domains is taken to be Set S , and the forgetful functor U S : Sys S Set S forgets the interpretations of the algebraic operations and the arrow composition, i.e. mapping each category to its set of arrows. Constraint Logic 13 Horn Clause Logic. In (Diaconescu, 1990) we introduce an embedding of the category of models M od S;P of a first order signature (S;S;P) as a retract of the category of algebras of an MSA signature (S b ; S b [P b ) obtained from the original first order signature by turning predicates into operations. Interpreting predicates as ....

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Diaconescu, R. (1996c). Completeness of semantic paramodulation: a category-based approach. Technical Report IS-RR-96-0006S, Japan Advanced Institute for Science and Technology.

.... specification, for equational logic we refer to [27] and for rewriting logic to [34] In the case of rewriting logic the relationship between the proof calculus and rewriting is very intimate, but for equational logic the completeness of rewriting can be found, among other many places, in [18, 10]. 5 Programming in the Large In this section we survey the semantics of the module interconnection system. CafeOBJ module interconnection system follows the principles of the OBJ module system which are inherited from earlier work on Clear [3] Consequently our semantics is based on institutions ....

Razvan Diaconescu. Completeness of semantic paramodulation: a category-based approach. Technical Report IS-RR-96-0006S, Japan Advanced Institute for Science and Technology, 1996.

.... specification, for equational logic we refer to [25] and for rewriting logic to [32] In the case of rewriting logic the relationship between the proof calculus and rewriting is very intimate, but for equational logic the completeness of rewriting can be found, among other many places, in [18, 7]. Notice that hidden logics of the CafeOBJ cube do not admit a complete (finitary) proof calculus. However, advanced proof techniques support the verification process in the case of behavioural specifications, most notably the hidden coinduction method (see [22] for the original definition, 12, ....

Razvan Diaconescu. Completeness of semantic paramodulation: a category-based approach. Technical Report IS-RR-96-0006S, Japan Advanced Institute for Science and Technology, 1996.

....are evident, for example the Logic 1.2 Constraint Logic and Category based Equational Logic The main idea of this research is to propose a logical system underlying ECLP; this is called constraint logic. We show that constraint logic can be naturally embedded into category based equational logic [9, 17, 10, 13, 12]. In this way, ECLP is integrated into equational logic programming, which is a stable and well understood programming paradigm possesing an important body of implementation techniques well integrated with its semantics. Although this integration is achieved at the level of abstract mathematical ....

....well integrated with its semantics. Although this integration is achieved at the level of abstract mathematical structures, therefore being merely semantic, it also has interesting computational implications due to the treatment of operational semantics for category based equational logic (see [13] and Chapter 4 of [9] Moreover, constraint logic might provide the right semantic framework for systems combining decision procedures (or constraint solvers) over different data types (see [11] This is based on institutions and on the OBJ approach on modules. The fact that constraint logic ....

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Razvan Diaconescu. Completeness of semantic paramodulation: a category-based approach. Technical Report IS-RR-96-0006S, Japan Advanced Institute for Science and Technology, 1996.

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