
Authors:
Zoltán MOLNÁR
Title:Induced Cylindric Algebras of Choice Structures
Pages:119127
File:bibtex
Abstract ( + )
One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Another implication of the axiom, discussed in the paper, is that an algebra is induced over the universe of the canonical model of a theory, which is isomorphic to a quotient algebra of the LindenbaumTarski algebra of the theory. Especially, in the case of Boolean or monadic algebras, the canonical model of the theory of a sigma complete model is isomorphic to the algebra induced by the axiom of extensionality.

Authors:
Piotr KULICKI
Title:On a Minimal System of Aristotle's Syllogistic
Pages:129145
File:bibtex
Abstract ( + )
The system of Syllogistic presented by J. Słupecki is a minimal, Łukasiewicz style system that includes all the theses present in Aristotle's writings. The axiomatic system is quite simple but it has no straightforward semantic counterpart. In the paper the semantics of the Słupecki's system is investigated: two approaches are used which lead to its two semantic characteristics. One is based on typically defined models, the other is a modelbased decision procedure, using the notion of a Horn formula.

Authors:
Ahmet HAMAL
Title:On the Logic of Closure Algebra
Pages:147163
File:bibtex
Abstract ( + )
An open problem in modal logic is to know if the fusion S4 ⊕ S4 is the complete modal logic for the product of any two metric separable denseinthemselves spaces. This would be settled, positively, if one could prove the following conjecture: When S4 is the complete logic for two complete atomic closure algebras, B and C, then the fusion S4 ⊕ S4 is the complete modal logic for their product B ⊗ C. This essay is an effort to give new garments to old results, in the hope that it would lead to a proof of this conjecture.

Authors:
Andrew SCHUMANN
Title:Two Squares of Opposition: for Analytic and Synthetic Propositions
Pages:165178
File:bibtex
Abstract ( + )
In the paper I prove that there are two squares of opposition. The unconventional one is built up for synthetic propositions. There a, i are contrary, a, o (resp. e, i) are contradictory, e, o are subcontrary, a,e (resp. i, o) are said to stand in the subalternation.

Authors:
Szymon FRANKOWSKI
Title:Partial and Intuitionistic Logic
Pages:179188
File:bibtex
Abstract ( + )
In the paper we propose a kind of interpretation of partial logic in the intuitionistic logic, or rather its part. We will show that finite binary trees determine this special fragment of intuitionistic logic.

Authors:
Thomas HENDREY
Title:Note on the Incompleteness of an Axiom System in Lewis' "Counterfactuals "
Pages:189193
File:bibtex
Abstract ( + )
I give a simple proof that an axiomatization of VC given in the original printing of Lewis' "Counterfactuals" is incomplete. I then briefly discuss its relationship to other axiomatizations Lewis gave.

Authors:
Gemma ROBLES, Francisco SALTO and José M. MÉNDEZ
Title:A Weak Logic with the Axiom Mingle Lacking theVariableSharing Property
Pages:195202
File:bibtex
Abstract ( + )
As it is well known, Relevance Logic R plus the axiom mingle (RMingle) does not have the variablesharing property (vsp). The aim of this paper is to improve this result by defining a weak logic with the axiom mingle and not included in minimal logic B_{M} lacking the vsp.

Authors:
Yehuda SCHWARTZ and George TOURLAKIS
Title:Pure Iteration and Substitution as the Basis of Computability
Pages:203213
File:bibtex
Abstract ( + )
It is known that, in the presence of pairing/projection functions, (pure) iteration can simulate primitive recursion [5, 6]. This fact implies that the class of primitive recursive functions,
, can be obtained as the closure of a small set of initial functions under
substitution and
pure iteration as long as the floor of the square root is included as an initial function to bootstrap the construction of pairing/projection functions or from just the successor and predecessor functions if we add
bounded search to the
a priori available operations. In Section~2 of the paper we show that neither the inclusion of square root nor of bounded search are necessary to build
from the successor and predecessor. In Section~3 we show that the class of partial recursive functions,
, can be obtained as the closure of
under the operation of infinite (pure) iteration.