Results 61 to 70 of about 155 (78)

Interpolation in Algebraizable Logics Semantics for Non-Normal Multi-Modal Logic

Journal of Applied Non-Classical Logics, 1998
ABSTRACT The two main directions pursued in the present paper are the following. The first direction was (perhaps) started by Pigozzi in 1969. In [Mak 91] and [Mak 79] 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.
exaly   +2 more sources

On the Algebraizability of Annotated Logics

Studia Logica, 1997
The authors introduce a structural version of annotated logics (introduced by V. S. Subrahmanian as logic foundation of computer programming) and prove that they are equivalent to the original systems, in the sense that everything provable in a system of one type has a translation that is provable in the corresponding system of the other types.
Renato A. Lewin, Irene F. Mikenberg, María G. Schwarze   +2 more
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Weakly algebraizable logics

Journal of Symbolic Logic, 2000
AbstractIn the paper we study the class of weakly algebraizable logics, characterized by the monotonicity and injectivity of the Leibniz operator on the theories of the logic. This class forms a new level in the non-linear hierarchy of protoalgebraic logics.
Janusz Czelakowski, Ramon Jansana
openaire   +1 more source

On semilattice-based logics with an algebraizable assertional companion. [PDF]

Reports Math. Log., 2011
This paper studies some properties of the so-called semilattice-based logics (which are defined in a standard way using only the order relation from a variety of algebras that have a semilattice reduct with maximum) under the assumption that its ...
Font, Josep Maria
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Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

Studia Logica, 1997
In this paper the author characterizes the hierarchy of protoalgebraic, equivalential, finitely equivalential, possibly infinitely algebraizable and finitely algebraizable logics by properties of the Leibniz operator. The author gives a new short proof of the main result of \textit{W. J. Blok} and \textit{D. Pigozzi} [Algebraizable logics, Mem.
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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.
openaire   +2 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.
openaire   +1 more source

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).
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Algebraizable logics

Memoirs of the American Mathematical Society, 1989
W. J. Blok, Don Pigozzi
openaire   +1 more source

Fragments of Quasi-Nelson: The Algebraizable Core

Logic Journal of the IGPL, 2022
Umberto Rivieccio, Rivieccio Umberto
exaly