
Authors:
Dolph ULRICH
Title:On Two Open Questions Concerning the Implicational Fragment of Rmingle
Pages:14
File:bibtex
Abstract ( + )
Two open questions concerning the implicational fragment of RMingle have been posed in the recent literature: does there exist a 2basis for this system, and does there exist a single axiom for it? Both questions are here answered affirmatively: CCCCpqqrCCrsCps together with CCCpCCCqprqrr provides a 2basis, and CCCCCCCpqrCqpCsrCsrCCttCuCvwCCxuCvCxw is a single axiom.

Authors:
George METCLAFE
Title:A Sequent Calculus for Constructive Logic with Strong Negation as a Substructural Logic
Pages:511
File:bibtex
Abstract ( + )
entzen systems are introduced for Spinks and Veroff's substructural logic corresponding to constructive logic with strong negation, and some logics in its vicinity.

Authors:
George TOURLAKIS
Title:A New Foundation of a Complete Boolean Equational Logic
Pages:1329
File:bibtex
Abstract ( + )
We redefine the equationalproofs formalism and present a direct proof that it is complete in the following strong and precise sense: Every tautology has an equational proof. As a sideeffect we establish that equational logic can be founded on a single rule of inference (Leibniz) without adding any axioms beyond those present in the foregoing references.

Authors:
Mohamed KHALED and Tarek Sayed AHMED
Title:Classes of Algebras that are not Closed under Completions
Pages:2943
File:bibtex
Abstract ( + )
e show that for several algebras studied in algebraic logic, the class of representable algebras of finite dimension >2 is not closed under completions. We prove an analogous result for many varieties that approximate the class of representable algebras. Our result applies to diagonal free cylindric algebras and polyadic algebras and all subreducts of polyadic algebras in between.

Authors:
Marek NASIENIEWSKI and Andrzej PIETRUSZCZAK
Title:New Axiomatizations of the Weakest Regular Modal Logic Defining Jaskowski's Logic D2
Pages:4550
File:bibtex
Abstract ( + )
In [Nasieniewski, Pietruszczak 2008] the weakest regular modal logic rS5^{M} defining D_{2} was indicated. The logic rS5^{M} was defined by means of a specific rule of inference (RM^{2}_{1}): ◊◊A/◊A. This rule was used in [Perzanowski 1975] to define S5^{M} — the weakest normal modal logic defining D_{2}. In [Blaszczuk, Dziobiak 1977] and [Nasieniewski 2002] an axiomatization of S5^{M} without this rule was given. In the present paper we axiomatize also rS5^{M} without the rule (RM^{2}_{1}). The present paper is a continuation of [Nasieniewski, Pietruszczak 2008].

Authors:
Henri GALINON
Title:A Note on Generalized Functional Completeness in the Realm of Elementary Logic
Pages:5159
File:bibtex
Abstract ( + )
In "Logicality and Invariance" (2008), Denis Bonnay introduced a generalized notion of functional completeness. In this note we call attention to an alternative characterization that is both natural and elementary.

Authors:
Gemma ROBLES and Jose M. MENDEZ
Title:The Basic Constructive Logic for Weak Consistency and the Reductio Axioms
Pages:6176
File:bibtex
Abstract ( + )
The aim of this paper is, on the one hand, to study the effect of adding the reductio axioms to the basic constructive logics adequate to the alternative concepts of consistency defined by us. On the other hand, this is a preliminary study on the, in some way, complicated relations these logics maintain to each other.

Authors:
J. Climent VIDAL and J. Soliveres TUR
Title:A Transformation between Institutions Representing the Theorem of HerbrandSchmidtWang
Pages:7794
File:bibtex
Abstract ( + )
We prove that domain unification, when viewed as a suitable transformation between two convenient institutions, represents the theorem of HerbrandSchmidtWang encoding manysorted firstorder logic into singlesorted firstorder logic.