Checking EMTLK Properties of Timed Interpreted Systems Via Bounded Model Checking

We investigate a SAT-based bounded model checking (BMC) method for EMTLK (the existential fragment of the metric temporal logic with knowledge) that is interpreted over timed models generated by timed interpreted systems. In particular, we translate the existential model checking problem for EMTLK to the existential model checking problem for a variant of linear temporal logic (called HLTLK), and we provide a SAT-based BMC technique for HLTLK. We evaluated the performance of our BMC by means of a variant of a timed generic pipeline paradigm scenario and a timed train controller system.     

Universality of the closure space of filters in the algebra of all subsets

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T ₀-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T ₀-closure spaces. By this theorem we obtain the following characterization of the consequence operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X.We assume the reader is familiar with notions in [5].     

A visually induced illusion of body tilt in a horizontal plane

Unexpected spontaneous reports of an illusion of body orientation have been observed in previous studies on the effects of a tilted overhead frame on supine observers. The present studies were designed in an attempt to describe and measure this illusion. The findings suggest that when objectively aligned with invisible side walls of the room, some subjects may experience an illusion that they are tilted in a horizontal plane with respect to the room walls in the direction opposite to frame tilt from the longitudinal body axes. The results are discussed in terms of a model of visual-vestibular interactions.     

Galois structures

This paper is a continuation of investigations on Galois connections from [1], [3], [10]. It is a continuation of [2]. We have shown many results that link properties of a given closure space with that of the dual space. For example: for every -disjunctive closure space X the dual closure space is topological iff the base of X generated by this dual space consists of the -prime sets in X (Theorem 2). Moreover the characterizations of the satisfiability relation for classical logic are shown. Roughly speaking our main result here is the following: a satisfiability relation in a logic L with, a countable language is a fragment of the classical one iff the compactness theorem for L holds (Theorems 3–8).     

Le traitement axiomatique de la notion de prolongement temporel

Sans résumé     

O niektórych nowych wynikach meta-matematycznych dotyczących teorii mnogości

Artykuł jest nieco zmienionym i rozszerzonym tekstem odczytu, wygłoszonego przez autora na sympozjum filozofii naukowej w Londynie w lipcu 1965. Angielski tekst odczytu ukaże się w sprawozdaniach z tego sympozjum. Allatum est die 23 Februarii 1966