The Skolem-Löwenheim theorem in toposes. II

This paper is a continuation of the investigation from [13]. The main theorem states that the general and the existential quantifiers are (, -reducible in some Grothendieck toposes. Using this result and Theorems 4.1, 4.2 [13] we get the downward Skolem-Löwenheim theorem for semantics in these toposes.     

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.     

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     

Sensorimotor synchronization: Motor responses to pseudoregular auditory patterns

Musically trained and untrained subjects (N=30) were asked to synchronize their finger tapping with stimuli in auditory patterns. Each pattern comprised six successive tonal stimuli of the same duration, the first of which was accented by a different frequency. The duration of interstimulus onset intervals (ISIs) gradually increased or decreased in constant steps toward the end of the patterns. Four values of such steps were used in different trials: 20, 30, 45, and 60 msec. Various time-control mechanisms are hypothesized as being simultaneously responsible for subjects’ incorrect reproduction of the internal temporal ratios of the stimulus patterns. The mechanism of assimilation (of a central tendency) led subjects to enforce a regular (isochronous) structure on the patterns. The influence of other time-control mechanisms (distinction, subjective expression of an accent, sequential transfer) was expressed mainly in differences between intertap onset intervals (ITIs) and the corresponding ISIs at the beginning of the patterns. The duration of the first two ITIs was in the majority of the trials in an inverse ratio to the ratio of the respective ISIs. The distortions resulting from the timing mechanisms concerned were more pronounced in the performance of nonmusicians than in that of musicians.     

Contrary-to-duty obligations

We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.