Results 61 to 70 of about 810,546 (73)

Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics

Studia Logica, 1997
This paper consists of three parts. In Part I, a new topological representation for general lattices is presented, and this representation is extended to a full duality. In Part II, the Jónsson and Tarski representation results for Boolean algebras with operators are extended for lattice-ordered algebras (lattices with additional operators).
Chrysafis Hartonas
openaire   +3 more sources

Categorical Abstract Algebraic Logic: Algebraizable Institutions

Applied Categorical Structures, 2002
The framework developed by W. J. Blok and D. Pigozzi for the algebraizability of deductive systems is extended to the algebraizability of multisignature logics with quantifiers.
G. Voutsadakis
openaire   +2 more sources

A Non-finitary Sentential Logic that is Elementarily Algebraizable

Journal of Logic and Computation, 2008
Summary: We exhibit a non-finitary sentential logic that is algebraized by a quasivariety -- in fact by a finitely based variety of finite type. The algebraization process requires infinitely many defining equations. The existence of such a logic settles a question posed by \textit{J. Czelakowski} [Protoalgebraic logics.
J. Raftery
openaire   +3 more sources

Omitting types for algebraizable extensions of first order logic

Journal of Applied Non-Classical Logics, 2005
We prove an Omitting Types Theorem for certain algebraizable extensions of first order logic without equality studied in [SAI 00] and [SAY 04]. This is done by proving a representation theorem preserving given countable sets of infinite meets for certain reducts of ω- dimensional polyadic algebras, the so-called G polyadic algebras (Theorem 5).
T. Ahmed
openaire   +2 more sources

Categorical Abstract Algebraic Logic: Ordered Equational Logic and Algebraizable PoVarieties

Order, 2007
This paper contains the fourth (and final) installment on research concerning an extension of some of the results on partially ordered varieties and quasi-varieties of partially ordered universal algebras obtained by Palasińska and Pigozzi in the context of abstract algebraic logic and reported in \textit{D.
George Voutsadakis, Voutsadakis George
exaly   +2 more sources

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
openaire   +3 more sources

THE ALGEBRAS OF LEWIS’S COUNTERFACTUALS: AXIOMATIZATIONS AND ALGEBRAIZABILITY

The Review of Symbolic Logic
The logico-algebraic study of Lewis’s hierarchy of variably strict conditional logics has been essentially unexplored, hindering our understanding of their mathematical foundations, and the connections with other logical systems. This work starts filling
Giuliano Rosella, Sara Ugolini
semanticscholar   +1 more source

Axiomatizing the Logic of Ordinary Discourse

arXiv.org
Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated by W.
V. Greati, Sérgio Marcelino, U. Rivieccio   +2 more
semanticscholar   +1 more source

Interpolation Properties, Beth Definability Properties and Amalgamation Properties for Substructural Logics

Journal of Logic and Computation, 2010
H. Kihara, H. Ono
semanticscholar   +1 more source

Three interpolation theorems for typeless logics

Logic Journal of the IGPL, 2012
T. Ahmed
semanticscholar   +1 more source