
Authors:
Wojciech DZIK, Beniamin WROBEL
Title:Unifiability in Relation Algebras and in Products of S5
Pages:114
File:bibtex
Abstract ( + )
Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties (in logics) are exhibited. Consequently, RA and products of S5 as well as representable diagonalfree ndimensional cylindric algebras, RDf_{n}, are almost structurally complete but not structurally complete. In case of S5_{n} a basis for admissible rules and the form of all passive rules are provided.

Authors:
Marcin LAZARZ, Krzysztof SIEMIENCZUK
Title:Note on some Characterization of Distributive Lattices of Finite Length
Pages:1517
File:bibtex
Abstract ( + )
Using known facts we give a simple characterization of the distributivity of lattices of finite length.

Authors:
Vladimir SHALACK
Title:On Some Applied FirstOrder Theories which Can be Represented by Definitions
Pages:1924
File:bibtex
Abstract ( + )
In the paper we formulate a sufficient criterion in order for the first order theory with finite set of axioms to be represented by definitions in predicate calculus. We prove the corresponding theorem. According to this criterion such theories as the theory of equivalence relation, the theory of partial order and many theories based on the equality relation with finite set of functional and predicate symbols are represented by definitions in the firstorder predicate calculus without equality.

Authors:
Rohan FRENCH and Lloyd HUMBERSTONE
Title:An Observation Concerning Porte's Rule in Modal Logic
Pages:2531
File:bibtex
Abstract ( + )
It is well known that no consistent normal modal logic contains (as theorems) both ⋄A and ⋄¬A (for any formula A). Here we observe that this claim can be strengthened to the following: for any formula A, either no consistent normal modal logic contains ⋄A, or else no consistent normal modal logic contains ⋄¬A.

Authors:
George VOUTSADAKIS
Title:Categorical Abstract Algebraic Logic Referential πInstitutions
Pages:3351
File:bibtex
Abstract ( + )
Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of algebraic and matrix semantics of arbitrary sentential logics. A wellknown theorem of Wójcicki asserts that a logic has a referential semantics if and only if it is selfextensional. Referential semantics was subsequently studied in detail by Malinowski and the concept of selfextensionality has played, more recently, an important role in the field of abstract algebraic logic in connection with the operator approach to algebraizability. We introduce and review some of the basic definitions and results pertaining to the referential semantics of πinstitutions, abstracting corresponding results from the realm of propositional logics.

Authors:
Andrzej BILAT
Title:NonFregean Logics of Analytic Equivalence I
Pages:5368
File:bibtex
Abstract ( + )
The identity connective is usually interpreted in nonFregean logic as an operator representing the identity of situations. This interpretation is related to the modal criterion of the identity of sentence correlates, characteristic of the WT system and some stronger systems. However, this connective can also be interpreted in a different way  as an operator representing the identity of propositions. The ``propositional" interpretation is in turn associated with the modalcontents criterion of the identity of sentence correlates. This begs the question of whether there is a system of nonFregean logic, providing an adequate formalization of this criterion. The aim of the paper is to systematize the metalogical and philosophical context of the issue and to point to a system that provides its solution.

Authors:
Andrzej BILAT
Title:NonFregean Logics of Analytic Equivalence II
Pages:6979
File:bibtex
Abstract ( + )
This paper presents the main assumptions of Andrzej Grzegorczyk's last research project concerning the logic of synonymity. It shows that the basis of logic of analytic equivalence, presented in the first part of the work, fully corresponds with these assumptions.

Authors:
G. C. RAO, Venugopalam UNDURTHI
Title:Closure Operators on Complete Almost Distributive LatticesIII
Pages:8193
File:bibtex
Abstract ( + )
In this paper, we prove that the lattice of all closure operators of a complete Almost Distributive Lattice L with fixed maximal element m is dual atomistic. We define the concept of a completely meetirreducible element in a complete ADL and derive a necessary and sufficient condition for a dual atom of Φ(L) to be complemented.