In [1] Chapter IV Lukasiewicz presents a system of syllogistic which is an extension of Aristotle’s ordinary syllogistic. In spite of this difference Lukasiewicz speaks about it, as do we, as the Aristotelian system. One of the well-known interpretation of syllogistic is Leibnitz’s interpretation described in [1] (pp. 126–129). Syllogistic formulas are interpreted there in an arithmetical manne...

In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix)....

Mobile robots generally have only incomplete knowledge about their world. This knowledge is augmented through sensing actions. There have been several approaches in reasoning about actions that deal with sensing and knowledge. One important approach, which has been successfully realized on a robotic soccer team, is based on autoepistemic description logics. In this paper, we present a probabili...

We introduce the generic Lah polynomials $L_{n,k}(\phi)$, which enumerate unordered forests of increasing ordered trees with a weight $\phi_i$ for each vertex $i$ children. show that, if sequence $\phi$ is Toeplitz-totally positive, then triangular array totally positive and row-generating $L_n(\phi,y)$ coefficientwise Hankel-totally positive. Upon specialization we obtain results symmetric fun...

Carcinogenesis is a complex process that involves dynamically inter-connected modular subnetworks that evolve under the influence of micro-environmental, as well as, in many cases, cancer therapy-induced perturbations, in non-random, pseudo-Markov chain processes. An appropriate n-stage model of carcinogenesis involves therefore n-valued Logic treatments of such processes, nonlinear dynamic tra...

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refuta...

Tarski’s Claim (TC = Theorem 8 in [13]) follows from simple considerations in (type-free) lambda-calculus. The present note records essentially a proof of Lemma 1.1 in [16], i.e. TCL = the type-free lambdacalculus variant of TC, as well as a few historical comments appearing there. Additional remarks are meant to insure the fact that TCL can be transferred verbatim to typed lambda-calculus [TCL...

There are few Romanian mathematicians (computer scientists) having seven books published by important international publishers. Professor Sergiu Rudeanu is one of them. He has several titles published by Springer, North-Holland, World Scientific, Dunod (Paris), Kogaku Tosho (Tokyo) and Bentham (eBooks). As well as several others books printed by wellknown Romanian publishers. Their titles refle...