Some Remarks on Relations between Proofs and Games

International audienceThis paper aims at studying relations between proof systems and games in a given logic and at analyzing what can be the interest and limits of a game formulation as an alternative semantic framework for modelling proof search and also for understanding relations between logics. In this perspective, we firstly study proofs and games at an abstract level which is neither related to a particular logic nor adopts a specific focus on their relations. Then, in order to instantiate such an analysis, we describe a dialogue game for intu-itionistic logic and emphasize the adequateness between proofs and winning strategies in this game. Finally, we consider how games can be seen to provide an alternative formulation for proof search and we stress on the possible mix of logical rules and search strategies inside games rules. We conclude on the merits and limits of the game semantics as a tool for studying logics, validity in these logics and some relations between them. 2 Proofs and Games In this section, we present a common terminology to present both proof systems and games at a relatively abstract level. Our aim consists in obtaining tools on which bridges can be built between the proof-theoretical approach and the game semantics approach in establishing the (universal) validity of logical formulae. We explain how proofs and games can be viewed as complementary notions. We illustrate how proof trees in calculi correspond to winning strategies in games and vice-versa

Detection and proof of cybercrime

Analysis findings in the field of cybercrime in the world and Ukraine as well prove a steady trend towards its growth, which causes a systematic increase in the number of victims affected by illegal malpractice of cyber criminals. This negative phenomenon violates not only citizens’ interests guaranteed by law, but also poses a threat to the national security in many countries. At the same time, international order is undermined and sustainable interstate relations are violated. Rapid information system development, speedy progress of computer software and hardware prompt numerous crimes in this field. Cybercrimes are committed by trained persons with a high intelligence level and professional knowledge in the computer technology sphere. In accordance with foregoing the issue of law approximation and the procedure of identification and recording of the mentioned illegal activity is essential to eradicate cybercrime. Considering the fact that the category of “proof” is fundamental in the theory of criminal procedure, we build in general-theoretical approaches in the basics of the analysis of the procedure of cybercrimes identification and recording to the mentioned activity in general

A domain-theoretic investigation of posets of sub-sigma-algebras (extended abstract)

Given a measurable space (X, M) there is a (Galois) connection between sub-sigma-algebras of M and equivalence relations on X. On the other hand equivalence relations on X are closely related to congruences on stochastic relations. In recent work, Doberkat has examined lattice properties of posets of congruences on a stochastic relation and motivated a domain-theoretic investigation of these ordered sets. Here we show that the posets of sub-sigma-algebras of a measurable space do not enjoy desired domain-theoretic properties and that our counterexamples can be applied to the set of smooth equivalence relations on an analytic space, thus giving a rather unsatisfactory answer to Doberkat's question