Results 221 to 230 of about 16,441 (253)

On the Algebraizability of the Implicational Fragment of Abelian Logic

Studia Logica, 2013
In this paper we consider the implicational fragment of Abelian logic A→. We show that although the Abelian groups provide an semantics for the set of theorems of A→ they do not for the associated consequence relation. We then show that the consequence relation is not algebraizable in the sense of Blok and Pigozzi (Mem Am Math Soc 77, 1989).
Butchart, Sam, Rogerson, Susan
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Quantum Logic as a Fragment of Independence-Friendly Logic

Journal of Philosophical Logic, 2002
The author presents his hypothesis that noncommuting variables are irreducibly interdependent in the logic connected with the foundations of quantum mechanics. The logic of such dependence relations is presented as independence-friendly logic, previously introduced by the author, which uses a sentence-initial contradictory negation over and above the ...
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Modal Logic and the Two-Variable Fragment

2001
We introduce a modal language L which is obtained from standard modal logic by adding the difference operator and modal operators interpreted by boolean combinations and the converse of accessibility relations. It is proved that L has the same expressive power as the two-variable fragment FO^2 of first-order logic but speaks less succinctly about ...
Carsten Lutz, Ulrike Sattler, Frank Wolter   +2 more
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Interpolation in fragments of classical linear logic

Journal of Symbolic Logic, 1994
AbstractWe study interpolation for elementary fragments of classical linear logic. Unlike in intuitionistic logic (see [Renardel de Lavalette, 1989]) there are fragments in linear logic for which interpolation does not hold. We prove interpolation for a lot of fragments and refute it for the multiplicative fragment (→, +), using proof nets and quantum ...
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A correspondence between implicational fragment logics and fuzzy logics

2014 IEEE International Conference on Granular Computing (GrC), 2014
This research report treats a correspondence between implicational fragment logics and fuzzy logics from the viewpoint of their algebraic semantics. The authors introduce monotone BI-algebras by loosening the axiomatic system of BCK-algebras. Also, we extend the algebras of fuzzy logics with weakly-associative conjunction from the case of the unit real
Mayuka F. Kawaguchi, Michiro Kondo
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Algebraic Characterizations for Universal Fragments of Logic

Mathematical Logic Quarterly, 1999
AbstractIn this paper we address our efforts to extend the well‐known connection in equational logic between equational theories and fully invariant congruences to other–possibly infinitary–logics. In the special case of algebras, this problem has been formerly treated by H. J. Hoehnke [10] and R. W. Quackenbush [14].
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Translating Separation Logic into a Fragment of the First-Order Logic

2010 Sixth International Conference on Semantics, Knowledge and Grids, 2010
Separation logic is an extension of Hoare logic for reasoning about mutable heap structure. To represent separation logic in the first-order logic, there are several choices to determine what are constants, what are predicates and quantifiers, and whether the commands are taken as atomic or composite.
Yuefei Sui, Yuming Shen, Cungen Cao, Ju Wang 0005   +3 more
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THE RELEVANT FRAGMENT OF FIRST ORDER LOGIC

The Review of Symbolic Logic, 2015
AbstractUnder a proper translation, the languages of propositional (and quantified relevant logic) with an absurdity constant are characterized as the fragments of first order logic preserved under (world-object) relevant directed bisimulations. Furthermore, the properties of pointed models axiomatizable by sets of propositional relevant formulas have ...
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On fragments of Medvedev's logic

Studia Logica, 1981
Medvedev's intermediate logic (MV) can be defined by means of Kripke semantics as the family of Kripke frames given by finite Boolean algebras without units as partially ordered sets. The aim of this paper is to present a proof of the theorem: For every set of connectivesΦ such that\(\{ \to , \vee , \urcorner \} \not \subseteq \Phi \subseteq \{ \to ...
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Logic Programming in a Fragment of Intuitionistic Temporal Linear Logic

2001
Recent development of logic programming languages based on linear logic suggests a successful direction to extend logic programming to be more expressive and more efficient. The treatment of formulasas-resources gives us not only powerful expressiveness, but also efficient access to a large set of data.
Mutsunori Banbara, Kyoung-Sun Kang, Takaharu Hirai, Naoyuki Tamura   +3 more
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