A formal ontology of situations

A generalized Wittgensteinian semantics for propositional languages is presented, based on a lattice of elementary situations. Of these, maximal ones are possible worlds, constituting a logical space; minimal ones are logical atoms, partitioned into its dimensions. A verifier of a proposition is an elementary situation such that if real it makes true. The reference (or objective) of a proposition is a situation, which is the set of all its minimal verifiers. (Maximal ones constitute its locus.) Situations are shown to form a Boolean algebra, and the Boolean set algebra of loci is its representation. Wittgenstein's is a special case, admitting binary dimensions only.     

The theory of boolean algebras with an additional binary operation

This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.The paper consists of two parts. At the beginning of the first one, several subclasses ofB-algebras are distinguished, and then, their basic properties, connections between them as well as certain relationships with other algebras, are investigated. In particular, it is shown that the class of Boolean algebras together with an arbitrary unary operation is polynomially equivalent to the class ofB ₁-algebras.The second part of the paper is concerned with the theory of filters and congruences inB-algebras.     

Logical space and metaphysical systems

The paper applies the theory presented in “A Formal Ontology of Situations” (this journal, vol. 41 (1982), no. 4) to obtain a typology of metaphysical systems by interpreting them as different ontologies of situations. Four are treated in some detail: Hume's diachronic atomism, Laplacean determinism, Hume's synchronic atomism, and Wittgenstein's logical atomism. Moreover, the relation of that theory to the “situation semantics” of Perry and Barwise is discussed.     

There are2^{\aleph _0 } logics with the relevance principle betweenR andRM

The aim of the paper is to prove the result announced by the title.     

Semantics in Banach spaces

A new approach to semantics, based on ordered Banach spaces, is proposed. The Banach spaces semantics arises as a generalization of the four particular cases: the Giles' approach to belief structures, its generalization to the non-Boolean case, and “fuzzy extensions” of Boolean as well as of non-Boolean semantics.     

Higher reflexes

The term reflex is used in a broad sense. Reflexes having a drive component are denoted as higher. Four types of higher reflexes are distinguished: avoidance, escape approach and consummately. Each of these reflexes has a different drive component. The result of the reflex is a removal of the corresponding drive. For this purpose three different strategies are used. Complex higher reflexes are usually programmed and occur frequently in a chain form. A given function of an organism is performed by a system of reflexes controlled by one or more drives.     

The degrees of maximality of the intuitionistic propositional logic and of some of its fragments

Professor Ryszard Wójcicki once asked whether the degree of maximality of the consequence operationC determined by the theorems of the intuitionistic propositional logic and the detachment rule for the implication connective is equal to \(2^{2^\aleph 0} \) ? The aim of the present paper is to give the affirmative answer to the question. More exactly, it is proved here that the degree of maximality ofC _Ψ — theΨ — fragment ofC, is equal to \(2^{2^\aleph 0} \) , for every such that → εΨ.     

A deduction theorem schema for deductive systems of propositional logics

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) _s q.