Computing Truth of Logical Statements in Multi-Agents’ Environment

Thispaperdescribeslogical models and computational algorithmsforlogical statements(specs) including various versions ofChanceDiscovery(CD).The approachisbased attemporal multi-agentlogic. Prime question is how to express most essential properties of CD in terms of temporal logic (branching time multi-agents’ logic or a linear one), how to define CD by formulas in logical language. We, as an example, introduce several formulas in the language of temporal multi-agent logic which may express essential properties of CD. Then we study computational questions (in particular, using some light modification of the standard filtration technique we show that the constructed logic has the finite-model property with effectively computable upper bound; this proves that the logic is decidable and provides a decision algorithm). At the final part of the paper we consider interpretation of CD via uncertainty and plausibility in an extension ofthelineartemporallogicLTL and computationfortruth values(satisfiability) ofits formulas.Представленная статья посвящена построению логических моделей различных версий теории случайных открытий (СО) и описанию вычислительных алгоритмов для логических высказываний. Предлагаемый нами подход основывается на многоагентной временной логике. Главный вопрос состоит в том, как можно было бы выразить самые существенные свойства СО в терминах временной логики, многоагентной логики с ветвящимся временем или линейной логики и вообще как определить СО с помощью формул языка логики. Нами в статье введено несколько формул на языке многоагентной временной логики, которые способны выразить существенные свойства СО. Используя некоторую модифицированную стандартную технику фильтрации, мы показали, что сконструированная таким образом логика имеет свойство финитной аппроксимируемости с эффективно вычислимой верхней границей. Это доказывает, что такая логика разрешима и нами предъявлен алгоритм разрешения. В заключительной части статьи мы рассматриваем интерпретацию СО посредством неопределённости и вероятности в расширении временной линейной логики и вычисление истинностных значений её формул

Crossing the Undecidability Border with Extensions of Propositional Neighborhood Logic over Natural Numbers

Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen's relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIME-complete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen's relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak first-order extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of first-order formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar first-order extensions of point-based temporal logics)

A Quantitative Extension of Interval Temporal Logic over Infinite Words

Model checking (MC) for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics (state-based, trace-based and tree-based semantics), all of them assuming homogeneity in the propositional valuation. Here, we focus on the trace-based semantics, where the main semantic entities are the infinite execution paths (traces) of the given Kripke structure. We introduce a quantitative extension of HS over traces, called Difference HS (DHS), allowing one to express timing constraints on the difference among interval lengths (durations). We show that MC and satisfiability of full DHS are in general undecidable, so, we investigate the decidability border for these problems by considering natural syntactical fragments of DHS. In particular, we identify a maximal decidable fragment DHSsimple of DHS proving in addition that the considered problems for this fragment are at least 2Expspace-hard. Moreover, by exploiting new results on linear-time hybrid logics, we show that for an equally expressive fragment of DHSsimple, the problems are Expspace-complete. Finally, we provide a characterization of HS over traces by means of the one-variable fragment of a novel hybrid logic

Cooperative Task Planning of Multi-Agent Systems Under Timed Temporal Specifications

In this paper the problem of cooperative task planning of multi-agent systems when timed constraints are imposed to the system is investigated. We consider timed constraints given by Metric Interval Temporal Logic (MITL). We propose a method for automatic control synthesis in a two-stage systematic procedure. With this method we guarantee that all the agents satisfy their own individual task specifications as well as that the team satisfies a team global task specification.Comment: Submitted to American Control Conference 201

Modeling Time in Computing: A Taxonomy and a Comparative Survey

The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only in the computer science domain, but also in more traditional fields of engineering. This article surveys various approaches to the formal modeling and analysis of the temporal features of computer-based systems, with a level of detail that is suitable also for non-specialists. In doing so, it provides a unifying framework, rather than just a comprehensive list of formalisms. The paper first lays out some key dimensions along which the various formalisms can be evaluated and compared. Then, a significant sample of formalisms for time modeling in computing are presented and discussed according to these dimensions. The adopted perspective is, to some extent, historical, going from "traditional" models and formalisms to more modern ones.Comment: More typos fixe

Controller synthesis for reactive systems in distributed, real-time and hybrid settings

Ph.DDOCTOR OF PHILOSOPH

Completeness of Flat Coalgebraic Fixpoint Logics

Modal fixpoint logics traditionally play a central role in computer science, in particular in artificial intelligence and concurrency. The mu-calculus and its relatives are among the most expressive logics of this type. However, popular fixpoint logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the mu-calculus. The family of such flat fixpoint logics includes, e.g., LTL, CTL, and the logic of common knowledge. Extending this notion to the generic semantic framework of coalgebraic logic enables covering a wide range of logics beyond the standard mu-calculus including, e.g., flat fragments of the graded mu-calculus and the alternating-time mu-calculus (such as alternating-time temporal logic ATL), as well as probabilistic and monotone fixpoint logics. We give a generic proof of completeness of the Kozen-Park axiomatization for such flat coalgebraic fixpoint logics.Comment: Short version appeared in Proc. 21st International Conference on Concurrency Theory, CONCUR 2010, Vol. 6269 of Lecture Notes in Computer Science, Springer, 2010, pp. 524-53