Wyniki wyszukiwania - Biblioteka Nauki

1

A Resolution Calculus for First-order Schemata

100%

Aravantinos V. , Echenim M. , Peltier N.

Fundamenta Informaticae

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2013

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tom Vol. 125, nr 2

101--133

EN

We devise a resolution calculus that tests the satisfiability of infinite families of clause sets, called clause set schemata. For schemata of propositional clause sets, we prove that this calculus is sound, refutationally complete, and terminating. The calculus is extended to first-order clauses, for which termination is lost, since the satisfiability problem is not semi-decidable for nonpropositional schemata. The expressive power of the considered logic is strictly greater than the one considered in our previous work.

2

Asymptotic Properties of Logics

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Zaionc M.

Schedae Informaticae

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2003

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tom Vol. 12

129-138

EN

This paper presents the number of results concerning problems of asymptotic densities in the variety of propositional logics. We investigate, for propositional formulas, the proportion of tautologies of the given length n against the number of all formulas of length n. We are specially interested in asymptotic behavior of this fraction. We show what the relation between a number of premises of an implicational formula and asymptotic probability of finding a formula with this number of premises is. Furthermore we investigate the distribution of this asymptotic probabilities. Distribution for all formulas is contrasted with the same distribution for tautologies only.

3

Valuation graphs for propositional logic

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Stępień L.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2010

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tom Vol. 15

139--148

EN

In this paper we present the proof system, called the valuation graphs system, which is a new version of two proof procedures: Davis-Putnam and Stålmarck. The novelty is that in the rules we note which propositional variable occurring in some propositional formula does not determine the logical value of that formula. Due to Stålmarck, we define a notion of proof width, corresponding to the width of structure of valuation graph which is a number of applications of dilemma rule. The dilemma rule considers two cases, so the time of proof grows up exponentially.

4

On Inferences of Full First-Order Hierarchical Decompositions

88%

Link S.

Fundamenta Informaticae

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2011

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tom Vol. 106, nr 2-4

233-258

EN

Database design aims to find a database schema that permits the efficient processing of common types of queries and updates on future database instances. Full first-order hierarchical decompositions constitute a large class of database constraints that can provide assistance to the database designer in identifying a suitable database schema. We establish finite axiomatisations of full first-order hierarchical decompositions that mimic best database design practice. That is, an inference engine derives all the independent collections of the universal schema during database normalization, and the designer determines during database denormalization which re-combinations of these independent collections manifest the final database schema. We also show that well-known correspondences between multivalued dependencies, degenerated multivalued dependencies, and a fragment of Boolean propositional logic do not extend beyond binary full first-order hierarchical decompositions.

5

Traktát Stanislava ze Znojma „De vero et falso“

88%

Sousedík S.

Filosofický časopis (Philosophical Journal)

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2015

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tom 63

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nr 6

831-857

EN

Stanislav of Znojmo (died 1414), a professor of the Prague Theological Faculty, first a teacher and friend to Jan Hus, but then his decided opponent, wrote a comprehensive treatise, probably around 1403, entitled De vero et falso. The subject of my article is an analysis of the content of this work. In it, Stanislav deals with the question of the truth of a proposition and the problem of its truth-maker. The question of the truth-maker falls into the area of metaphysics, and so the author speaks of metaphysical truth. In so far as metaphysical truth is concerned, Stanislav of Znojmo defends a decidedly realist standpoint, judging that categorematic expressions are not alone in having real counterparts in the world, but syncategorematic expressions (for example, statement conjunctions, words expressing negations and so on) also have such counterparts. Stanislav’s treatise, in its overall orientation, belongs to propositionalism, a trend in logical thought widespread at the end of the Middle Ages. Although the author of the treatise De vero et falso does not cite contemporary authors, he shows a knowledge of some exponents of propositional logic (namely Gregory of Rimini, for example). His main inspiration, however, is undoubtedly the work of John Wyclif.

6

A propositional logic of temporal connectives

88%

Epstein R. L. , Buitrago-Díaz E.

Logic and Logical Philosophy

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2015

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tom 24

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nr 2

155–200

EN

We investigate how to formalize reasoning that takes account of time by using connectives like “before” and “after.” We develop semantics for a formal logic, which we axiomatize. In proving that the axiomatization is strongly complete we show how a temporal ordering of propositions can yield a linear timeline. We formalize examples of ordinary language sentences to illustrate the scope and limitations of this method. We then discuss ways to deal with some of those limitations.

7

Dowody metodą tableaux

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Szyper L.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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1999

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tom Vol. 6

107--115

8

Teoria kategorii i niektóre jej logiczne aspekty

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Stopa M.

Zagadnienia Filozoficzne w Nauce

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2018

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nr 64

7-58

PL

This article is intended for philosophers and logicians as a short partial introduction to category theory (CT) and its peculiar connection with logic. First, we consider CT itself. We give a brief insight into its history, introduce some basic definitions and present examples. In the second part, we focus on categorical topos semantics for propositional logic. We give some properties of logic in toposes, which, in general, is an intuitionistic logic. We next present two families of toposes whose tautologies are identical with those of classical propositional logic. The relatively extensive bibliography is given in order to support further studies.

9

A meta-logic of inference rules: Syntax

75%

Citkin A.

Logic and Logical Philosophy

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2015

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tom 24

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nr 3

313–337

EN

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and especially the presence of the rule of reverse substitution, requires certain change the definition of structurality.

10

Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations

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Pynko A. P.

Bulletin of the Section of Logic

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2020

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tom 49

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nr 4

401-437

EN

Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 𝔄4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable Sharing Property (VSP). We then characterize L4's having a theorem / inconsistent formula, satisfying VSP and being [inferentially] maximal / subclassical / maximally paraconsistent, in particular, algebraically through ℳ4|𝔄4's (not) having certain submatrices|subalebras. Likewise, [providing 𝔄4 is regular / has no three-element subalgebra] L4 has a proper consistent axiomatic extension if[f] ℳ4 has a proper paraconsistent / two-valued submatrix [in which case the logic of this submatrix is the only proper consistent axiomatic extension of L4 and is relatively axiomatized by the Excluded Middle law axiom]. As a generic tool (applicable, in particular, to both classically-negative and implicative expansions of DB4), we also prove that the lattice of axiomatic extensions of the logic of an implicative matrix ℳ with equality determinant is dual to the distributive lattice of lower cones of the set of all submatrices of ℳ with non-distinguished values.