Algebraic aspects of deduction theorems

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian.A part of this paper was presented in abstracted form in Bulletin of the Section of Logic, Vol. 12, No. 3 (1983), pp. 111–116, and in The Journal of Symbolic Logic.     

Behavior of visual evoked potentials (pattern reversal VECP) in smokers

Twenty six clinically healthy smokers were studied with transient pattern visual-evoked potentials. In comparison with a sample of "normal" subjects we found a difference of some parameters (P less than 0.05): the P2-latency and the interocular difference of latency on average were 6-7 ms respectively 2 ms larger. Thirteen subjects have had a prolonged P2-latency (P less than 0.05) and/or a difference in interocular latencies larger than 5 ms. These findings may suggest on subclinical disturbances of visual system and indicators of an special sensitivity of that person. The findings are possibly related to tobacco-alcohol amblyopia.     

A Nonmonotonic Modal Formalization of the Logic of Acceptance and Rejection

The problems we deal with concern reasoning about incomplete knowledge. Knowledge is understood as ability of an ideal rational agent to make decisions about pieces of information. The formalisms we are particularly interested in are Moore's autoepistemic logic (AEL) and its variant, the logic of acceptance and rejection (AEL2). It is well-known that AEL may be seen as the nonmonotonic KD45 modal logic. The aim is to give an appropriate modal formalization for AEL2.     

Unrealistic Optimism and Positive-Negative Asymmetry: A Conceptual and Cross-cultural Study of Interrelationships between Optimism,Pessimism, and Realism

Using a variant of Weinstein's (1980) technique for the measurement of unrealistic optimism, subjects were classified as optimistic, realistic, or pessimistic about their chances of being confronted in the future with problems such as divorce, nervous breakdown, etc. On the basis of previous theory and research on cognition and affect, it was hypothesized that, across problems, subjects would alternate optimism with realism rather than with pessimism. Cross-cultural data obtained from 19 samples of Belgian, Moroccan, and Polish subjects not only confirmed the hypothesis but also showed high agreement about the nature of the problems that were selectively associated with optimism, realism and pessimism.     

Three-element nonfinitely axiomatizable matrices

There are exactly two nonfinitely axiomatizable algebraic matrices with one binary connective o such thatx(yz) is a tautology of . This answers a question asked by W. Rautenberg in [2], P. Wojtylak in [8] and W. Dziobiak in [1]. Since every 2-element matrix can be finitely axiomatized ([3]), the matrices presented here are of the smallest possible size and in some sense are the simplest possible.Presented byWolfgang Rautenberg