
Authors:
George WEAVER and Benjamin R. GEORGE
Title:The FraenkelCarnap Question for Limited HigherOrderLanguages
Pages:19
File:bibtex
Abstract ( + )
In the late 20's Fraenkel and Carnap raised the question of whether or not all semantically complete finitely axiomatizable theories formulated in the theory of types are categorical. Carnap announced a positive answer to this question. However, that proof was flawed (see Awody and Carus [2001] and Awodey and Reck [2002]). The FraenkelCarnap question has been ignored until it was rediscovered by Awodey, Carus and Reck. Scott noticed that the question has a positive answer for theories formulated in those n^{}order languages (n ≥2) whose nonlogical vocabulary is empty. It is shown here that this question also has a positive answer when the nonlogical vocabulary is nonempty provided it includes only individual constants or monadic predicate constants.

Authors:
Jānis CĪRULIS
Title:Residuation Subreducts of Pocrigs
Pages:1116
File:bibtex
Abstract ( + )
A pocrig (A,·,→,1) is a partially ordered commutative residuated integral groupoid. We characterise the class of all residuation subreducts (A,→,1) of pocrigs.

Authors:
Sergey BABENYSHEV and Manuel A. MARTINS
Title:Admissible Equivalence Systems
Pages:1733
File:bibtex
Abstract ( + )
Whenever a logic is the set of theorems of some deductive system, where the latter has an equivalence system, the behavioral theorems of the logic can be determined by means of that equivalence system. In general, this original equivalence system may be too restrictive, because it suffices to check behavioral theorems by means of any admissible equivalence system (that is an equivalence system of the smallest deductive system associated with the given logic). In this paper, we present a range of examples, which show that: 1) there is an admissible equivalence system which is not an equivalence system for the initial deductive system, 2) there is a nonfinitely equivalential deductive system with a finite admissible equivalence system, and 3) there is a deductive system with an admissible equivalence systems, such that this deductive system is not even protoalgebraic itself. We use methods and results from algebraic and modal logic.

Authors:
Alexej P. PYNKO
Title:Gentzen's CutFree Calculus Versus the Logic of Paradox
Pages:3542
File:bibtex
Abstract ( + )
The main result of the paper is that the sequent calculus
obtained from Gentzen's LK by eliminating Cut and adding the rules inverse to logical ones is equivalent to the logic of paradox. As a consequence, we prove that LK and the sequent calculus
which results from adding instances of Cut without side formulas to
are the only proper consistent extensions of
.

Authors:
Gábor SÁGI
Title:AbsolutelyUbiquitous Structures and אi_{0}  Stability
Pages:4351
File:bibtex
Abstract ( + )
Continuing investigations initiated in [3], we will prove that a certain subclass of absolutely ubiquitous structures are א i_{0}  stable. This confirms a special case of a conjecture of Macpherson [5].

Authors:
Piotr KULICKI
Title:Hallden Incomplete Calculus of Names
Pages:5355
File:bibtex
Abstract ( + )
[Abstract]

Authors:
Anna BIEŃ
Title:Cycles in Nielsen's Graphs
Pages:5764
File:bibtex
Abstract ( + )
Nielsen's substitutions are usually used to calculate solutions of equations in free monoids. Each solution can be given as a composition of finitely many such substitutions. The process of solving defines the so called solution graph in which vertices are equations and edges correspond to Nielsen's substitutions. In this paper we deal with solution graphs containing cycles. The main theorem gives some restrictions on the number of variables occurring in equations of such graphs.

Authors:
Norihiro KAMIDE
Title:Strong Normalization of ProgramIndexed Lambda Calculus
Pages:6578
File:bibtex
Abstract ( + )
A programindexed typed λcalculus, λ_{DL}, is introduced. λ_{DL} has a CurryHoward correspondence with an intuitionistic variant of dynamic logics. The strong normalization theorem for λ_{DL} is proved.

Authors:
Gemma ROBLES and José M. MÉNDEZ
Title:AxiomatizingS4_{+} and J_{+} without the Suffixing, Prefixingand SelfDistribution of the Conditional Axioms
Pages:7991
File:bibtex
Abstract ( + )
In this note, we axiomatize the positive fragments of Lewis' S4, S4_{+}, and of intuitionistic logic, J_{+}, by extending Routley and Meyer's basic positive logic B_{+} with the contraction axiom and, respectively, the restricted K axiom and the K axiom.

Authors:
Ewa GRACZYŃSKA
Title:MHyperquasiIdentities of Finite Algebras
Pages:93102
File:bibtex
Abstract ( + )
n [4] (see [2]) the notion of a hypersubstitution of a given type and the notion of a it derived variety D(V) of a given variety V of a fixed type τ were invented. Suitable hyperequational calculus appeared as a modification of G. Birkhoff calculus with additional rule called hypersubstitution rule (6). In Graczyńska E. and Schweigert D. [6] we considered further generalization to Mhyperquasivarieties of a given type. Basing on the result of A. Wroński [11] we modify A. Selman calculus [10] and the Gentzenstyle calculus of [11] presenting a finite axiomatization of Mhyperquasiidentities of a finite algebra (of a finite type τ). The results were presented on the conference AAA79 and CYA25 Olomouc (Czech Republic), February 1214, 2010.