
Authors:
Yi ZHANG
Title:Remarks on a class of almost disjoint families
Pages:113
File:bibtex
Abstract ( + )
We study the relationship between several closely related m.a.d. families in several forcing models. We also prove some ZFC result concerning the lower bound of these m.a.d. families, which answers a question suggested by Stevo Todorcevic. In the last section, we state several open problems in this area.

Authors:
Kentaro KIKUCHI
Title:Relationships between basic propositional calculus and substructural logics
Pages:1520
File:bibtex
Abstract ( + )
An investigation of relationships between Basic Propositional Calculus (BPC) and substructural logics is made with the help of a system which characterizes the implicational fragment of BPC.

Authors:
Luis F. CACERESDUQUE
Title:Ideal theories of the ring of polynomials over the integres
Pages:2131
File:bibtex
Abstract ( + )
The definition of the propositional theories T^{δ}(R) associated with a commutative ring with identity R is given and the ultraproduct notion of sets is used to study these theories for the ring of polynomials over the integers. An axiomatization for T^{δ}(Z[x]) is found, models and atom models of T^{δ}(Z[x]) are described and it is demonstrate how each model of T^{δ}(Z[x]) is, in an effective way, an ultraproduct of these atom models of T^{δ}(Z[x]).

Authors:
Tomasz KOWALSKI
Title:Propositional dynamic logic has interpolation
Pages:3339
File:bibtex
Abstract ( + )
Interpolation theorem for propositional dynamic logic is proved solving a longstanding open question in the area.

Authors:
Nicholas ASHER and Yi MAO
Title:Negated defaults in commonsense entailment
Pages:4160
File:bibtex
Abstract ( + )
In this paper, we introduce two notions of nonmonotonic reasoning: the syntactic notion of reasonable consequence > and the semantic notion of Reasonable Entailment =>. We prove that one is sound and complete relative to the other. There are two layers involved in the definition of >: at the bottom is a propositional modal conditional logic which allows unlimited nesting of defaults and embedings into any context analyzable in possibleworlds semantics. > is built on the top of this system via the notion of deductive transformation closure. We show that the new definition of > is cumulative and satisfies a series of properties that a nonmonotonic inference relation is expected to have.