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Robert Goldblatt Topological Proofs of Some RasiowaSikorski Lemmas
"... Abstract. We give topological proofs of Görnemann’s adaptation to Heyting algebras of the RasiowaSikorski Lemma for Boolean algebras; and of the RauszerSabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire catego ..."
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Abstract. We give topological proofs of Görnemann’s adaptation to Heyting algebras of the RasiowaSikorski Lemma for Boolean algebras; and of the RauszerSabalski generalisation of it to distributive lattices. The arguments use the Priestley topology on the set of prime filters, and the Baire
Logic Programming from the Perspective of Algebraic Semantics
, 1996
"... . We present an approach to foundations of logic programming in which the connection with algebraic semantics becomes apparent. The approach is based on omegaHerbrand models instead of conventional Herbrand models. We give a proof of Clark's theorem on completeness of SLDresolution by methods ..."
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resolution by methods of the algebraic semantics. We prove the existence property for definite programs. Keywords: RasiowaSikorski lemma, algebraic semantics, logic programming, completeness of SLDresolution. 1. Introduction A part of work of Professor Helena Rasiowa was devoted to the development of methods
An Extension of the Lemma of Rasiowa and Sikorski
, 1997
"... We prove an extension of the Lemma of Rasiowa and Sikorski and give some applications. Moreover, we analyze its relationship to corresponding results on the omission of types. 1 Introduction Let B be a Boolean algebra, E ` B, and let a 2 B be the infimum of E, a = V E. An ultrafilter U preserv ..."
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We prove an extension of the Lemma of Rasiowa and Sikorski and give some applications. Moreover, we analyze its relationship to corresponding results on the omission of types. 1 Introduction Let B be a Boolean algebra, E ` B, and let a 2 B be the infimum of E, a = V E. An ultrafilter U
Strong Completeness for Markovian Logics
"... Abstract. In this paper we present Hilbertstyle axiomatizations for three logics for reasoning about continuousspace Markov processes (MPs): (i) a logic for MPs defined for probability distributions on measurable state spaces, (ii) a logic for MPs defined for subprobability distributions and (iii ..."
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the problem of proving strong completeness for these and similar logics. Unlike the CAR, our rule has a countable set of instances; consequently it allows us to apply the RasiowaSikorski lemma for establishing strong completeness. Our proof method is novel and it can be used for other logics as well. 1
THE COLLAPSE OF THE DESCRIPTIVE COMPLEXITY OF TRUTH DEFINITIONS. COMPLETIONS OF HEYTING AND BOOLEAN ALGEBRAS
"... We are interested in applying constructive methods in (classical and intuitionistic) model theory. We describe in a canonical way and in the frame of constructive metamathematics a procedure for an embedding with a small descriptive complexity of arbitrary Boolean (or Heyting) algebra in a complete ..."
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algebra, preserving all existing unions and meets. As a prehistory of the method we mention the work of Friedman (as it described in [1]) and the wellknown lemma of RasiowaSikorski about completing of Boolean algebras with preserving a given countable family of unions and meets. As an applications we