Elimination of Negation in Term Algebras
نویسندگان
چکیده
runtime form of constructive negation does not have this advantage, but applies to many more programs. The simple form of the runtime method 1], given a negative goal :A, executes A; if A has a nite SLD-tree with answer substitutions (as substitution formulas) s 1 collection of substitutions in cases as described by Theorem 5, but in general cannot be presented this way. For example, the goal :append(x; y; z:nil) must return as an answer :9v (x = nil ^ y = v:nil ^ z = v:nil) ^ :9v (x = v:nil ^ y = nil ^ z = v:nil). Thus, again, Theorem 5 forces upon us an execution mechanism capable of handling inequalities. The general runtime method faces the same problems. Since the use of constraints has many advantages 11] and substitutions are too weak to represent the appropriate negative information, most approaches to constructive negation are based on constraints 28, 19, 43, 1, 41], rather than substitutions. The algorithm uncover is useful for reducing :s 1 ^ : : : ^ :s m , and the formulas produced by the Sato-Tamaki transformation, to a \simplest" form, with only inequalities that, as the theorem shows, are unavoidable.
منابع مشابه
Quantifier Elimination in Term Algebras The Case of Finite Languages
We give a quantifier elimination procedure for term algebras over suitably expanded finite first-order languages. Our expansion is purely functional. Our method works by substituting finitely many parametric test terms. This allows us to obtain in addition sample solutions for an outermost existential quantifier block. The existence of our method implies that the considered quantifier eliminati...
متن کاملNegation and BCK-algebras
In this paper we consider twelve classical laws of negation and study their relations in the context of BCKalgebras. A classification of the laws of negation is established and some characterizations are obtained. For example, using the concept of translation we obtain some characterizations of Hilbert algebras and commutative BCK-algebras with minimum. As a consequence we obtain a theorem rela...
متن کاملCharacterisations of Nelson Algebras
Nelson algebras arise naturally in algebraic logic as the algebraic models of Nelson’s constructive logic with strong negation. This note gives two characterisations of the variety of Nelson algebras up to term equivalence, together with a characterisation of the finite Nelson algebras up to polynomial equivalence. The results answer a question of Blok and Pigozzi and clarify some earlier work ...
متن کاملThe Craig interpolation theorem for prepositional logics with strong negation
This paper deals with propositional calculi with strong negation(N-logics) in which the Craig interpolation theorem holds. N-logics are defined to be axiomatic strengthenings of the intuitionistic calculus enriched with a unary connective called strong negation. There exists continuum of N-logics, but the Craig interpolation theorem holds only in 14 of them. " A propositional calculus with stro...
متن کاملBoolean Algebras in Visser Algebras
We generalize the double negation construction of Boolean algebras in Heyting algebras, to a double negation construction of the same in Visser algebras (also known as basic algebras). This result allows us to generalize Glivenko’s Theorem from intuitionistic propositional logic and Heyting algebras to Visser’s basic propositional logic and Visser algebras. Mathematics Subject Classification: P...
متن کامل