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131.
GL-Quantales: Q-Valued Sets and Their Singletons 总被引:1,自引:0,他引:1
Ulrich Höhle 《Studia Logica》1998,61(1):123-148
Q-valued sets are non-classical models of the formalized theory of identity with existence predicate based on the axioms of a non-commutative and non-idempotent logic. The singleton monad on the category of Q-valued sets is constructed, and elementary properties of T-algebras of the singleton monad are investigated. 相似文献
132.
Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open.Related issues of universal algebra and of algebraic logic are discussed, too. In particular we investigate the possibility of extending the characterization of interpolability to arbitrary algebraizable logics. 相似文献
133.
Michael Kremer defines fixed-point logics of truth based on Saul Kripke’s fixed point semantics for languages expressing their own truth concepts. Kremer axiomatizes the strong
Kleene fixed-point logic of truth and the weak Kleene fixed-point logic of truth, but leaves the axiomatizability question
open for the supervaluation fixed-point logic of truth and its variants. We show that the principal supervaluation fixed point
logic of truth, when thought of as consequence relation, is highly complex: it is not even analytic. We also consider variants,
engendered by a stronger notion of ‘fixed point’, and by variant supervaluation schemes. A ‘logic’ is often thought of, not
as a consequence relation, but as a set of sentences – the sentences true on each interpretation. We axiomatize the supervaluation
fixed-point logics so conceived. 相似文献
134.
Antoni Torrens 《Studia Logica》2008,88(3):349-383
In a classical paper [15] V. Glivenko showed that a proposition is classically demonstrable if and only if its double negation
is intuitionistically demonstrable. This result has an algebraic formulation: the double negation is a homomorphism from each
Heyting algebra onto the Boolean algebra of its regular elements. Versions of both the logical and algebraic formulations
of Glivenko’s theorem, adapted to other systems of logics and to algebras not necessarily related to logic can be found in
the literature (see [2, 9, 8, 14] and [13, 7, 14]). The aim of this paper is to offer a general frame for studying both logical
and algebraic generalizations of Glivenko’s theorem. We give abstract formulations for quasivarieties of algebras and for
equivalential and algebraizable deductive systems and both formulations are compared when the quasivariety and the deductive
system are related. We also analyse Glivenko’s theorem for compatible expansions of both cases.
Presented by Jacek Malinowski 相似文献
135.
Nick Bezhanishvili 《Studia Logica》2008,90(2):139-159
In this paper we define the notion of frame based formulas. We show that the well-known examples of formulas arising from
a finite frame, such as the Jankov-de Jongh formulas, subframe formulas and cofinal subframe formulas, are all particular
cases of the frame based formulas. We give a criterion for an intermediate logic to be axiomatizable by frame based formulas
and use this criterion to obtain a simple proof that every locally tabular intermediate logic is axiomatizable by Jankov-de
Jongh formulas. We also show that not every intermediate logic is axiomatizable by frame based formulas.
Presented by Johan van Benthem 相似文献
136.
Dorota Leszczyńska-Jasion 《Studia Logica》2008,89(3):365-399
The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5.
Presented by Jacek Malinowski 相似文献
137.
In this article we deal with Glivenko type theorems for intuitionistic modal logics over Prior's MIPC. We examine the problems which appear in proving Glivenko type theorems when passing from the intuitionistic propositional logic Intto MIPC. As a result we obtain two different versions of Glivenko's theorem for logics over MIPC. Since MIPCcan be thought of as a one-variable fragment of the intuitionistic predicate logic Q-Int, one of the versions of Glivenko's theorem for logics over MIPCis closely related to that for intermediate predicate logics obtained by Umezawa [27] and Gabbay [15]. Another one is rather surprising. 相似文献
138.
Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various techniques that improve the efficiency of the basic naive method for such tableaux. 相似文献
139.
Three Complexity Problems in Quantified Fuzzy Logic 总被引:1,自引:0,他引:1
We prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01]. 相似文献
140.