
Authors:
Paulo A.S.VELOSO
Title:Why ultrafilters for almost all
Pages:183193
File:bibtex
Abstract ( + )
We discuss, trying to explain and justify, a fundamental issue in the precise treatment of assertions involving "almost all" objects. We address the contention of lack of intuitive justification for using ultrafilters to capture the intended meaning of almost all. We first reassess the ultrafilter proposal, suggesting an alternative interpretation. We then analyze some basic intuitions, which suggest a few postulates, leading naturally to the idea of ultrafilters.

Authors:
Francisco SALTO, Gemma ROBLES and Jose M. MENDEZ
Title:Exhaustively axiomatizing RMO_{>} with a select list of representative theses including restricted mingle principles
Pages:195206
File:bibtex
Abstract ( + )
RMO_{>} is the result of adding the `mingle principle' [i.e., A>(A>A)] to Anderson's and Belnap's implicative logic of relevance R_{>}. The aim of this paper is to provide all possible axiomatizations with independent axioms of RMO_{>} formulable with Anderson and Belnap's "strong and natural list of valid entailments" extended with ten characteristic minglish principles.

Authors:
Tomasz POLACIK
Title:Partiallyelementary extension Kripke models and Burr's hierarchy
Pages:207214
File:bibtex
Abstract ( + )
We investigate Kripke models of subtheories iΦ_{n} of Heyting Arithmetic. The theories iΦ_{n}, defined by W.Burr, can be regarded as the natural intuitionistic counterparts of subtheories IΠ_{n} of Peano Arithmetic. In the paper we consider nelementary extension Kripke models which are models whose worlds are ordered by the elementary extension relation with respect to Σ_{n} formulae instead of merely the (weak) submodel relation. We prove that every IΠ_{n}normal, nelementary extension model is a model of iΦ_{n}. This suggests a method of constructing nontrivial Kripke models of iΦ_{n}. We also show that every (n+1)elementary extension model of iΦ_{n} is IΠ_{n}normal.

Authors:
Janusz MACIASZEK
Title:A note on the concept of satisfaction in intuitionistic predicate logic
Pages:215223
File:bibtex
Abstract ( + )
The aim of the paper is to reconstruct Kripke semantics of Intuitionistic Predicate Logic without possible worlds. It can be done in terms of the Tarskian concept of satisfaction of a formula by a sequence which is usually considered as an alternative of a valuation of variables. It is not the case in the presented semantics, where a sequence plays a double role: of a valuation and of a possible world.

Authors:
Luiz Carlos P.D.PEREIRA and Edward Hermann HAEUSLER
Title:An infinitary extension of MALL^{}
Pages:225233
File:bibtex
Abstract ( + )
The aim of the present paper is to introduce an extension of the Multiplicative Fragment of Classical Propositional Linear Logic where infinitary versions of o and & are considered. We define the sequent calculus LIP_{inf} and prove its soundness and completeness with respect to an infinitary extension of Girard's Phase Semantics.