A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S5

The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.     

On the Complexity of Nonassociative Lambek Calculus with Unit

Nonassociative Lambek Calculus (NL) is a syntactic calculus of types introduced by Lambek [8]. The polynomial time decidability of NL was established by de Groote and Lamarche [4]. Buszkowski [3] showed that systems of NL with finitely many assumptions are decidable in polynomial time and generate context-free languages; actually the P-TIME complexity is established for the consequence relation of NL. Adapting the method of Buszkowski [3] we prove an analogous result for Nonassociative Lambek Calculus with unit (NL1). Moreover, we show that any Lambek grammar based on NL1 (with assumptions) can be transformed into an equivalent context-free grammar in polynomial time.     

Basic properties of the equivalence

In this paper we investigate some basic semantic and syntactic conditions characterizing the equivalence connective. In particular we define three basic classes of algebras: the class of weak equivalential algebras, the class of equivalential algebras and the class of regular equivalential algebras (see [12]).Weak equivalential algebras can be used to study purely equivalential fragments of relevant logics and strict equivalential fragments of some modal logics (for investigations of strict implicational fragments of modal logics see [20]). Equivalential algebras are suitable to study purely equivalential fragment of BCI and BCK logic (see [21], p. 316). A subclass of the class of regular equivalential algebras is suitable to study equivalential fragments of ukasiewicz logics. Some subvarieties of the class of regular equivalential algebras provide natural semantics for equivalential fragments of the intuitionistic prepositional logic and various intermediate logics (see [13]).The last chapter is a selection of research problems which in the author's opinion are worth to be solved.     

S. A. Janovskaja

With the passing of S. A. Janovskaja, contemporary Soviet philosophy has lost one of its leading experts in logic and in combining creativity with survival.     

Three-configuration matching-to-sample in the pigeon

Pigeons were trained on a zero-delay matching-to-sample procedure during which only three of the four possible stimulus configurations were presented. Subsequently, all birds were exposed to all four configurations as a transfer test. A high degree of negative transfer from the three training configurations was obtained in Experiment 1. The results of Experiment 2 indicated that three-configuration training produced differential position-preference effects. During the transfer test, responding after one sample stimulus was apparently based on position, while responding after the other sample was based on color.     

Epidemiology and psychopathology of epileptics in Bydgoszca Province registered between 1976 and 1980

In the years 1976-1980, the province of Bydgoszcz had a total of 2635 registered epileptics, or 0.37% of the entire population, over the age of 16. From these, 200 patients were randomly selected, and between 1983 and 1985 a complats clinical follow-up investigation was carried out. Among the most frequent mental disorders found were postparoxysmal twilight state (19.5%) and affective psychoses (11%), among the chronic disorders, dementia of varying intensity (26.5%). In contrast with previous investigations the present investigation made it possible to determine with precision the cause of epileptic attacks. The ratio was 61% to 31%.