Group Beliefs : Studies on the Nature and Logic of Collective Doxastic Attitudes

This thesis studies the nature and logic of collective doxastic attitudes, or what is referred to in ordinary language as "group beliefs". Beliefs and other intentional attitudes are attributed to groups and collections of people, and such attributions are used to explain and predict the actions of groups. The thesis develops an understanding of group beliefs as voluntarily adopted views or acceptances rather than as ordinary beliefs. Such an understanding can provide new answers to questions concerning collective knowledge and justification of group beliefs, and it allows developing modal logics with collective doxastic and epistemic notions. The thesis consists of six articles. The first three articles are philosophical studies concerned with the nature of group beliefs. The last three articles are logical studies that aim at developing proof-theoretical calculi for reasoning about collective doxastic attitudes.

When is `partial' adequate? A logic-based proof technique using partial specifications

A technique is presented for ascertaining when a (finite-state) partial process specification is adequate, in the sense of being specified enough, for contexts in which it is to be used. The method relies on the automatic generation of a modal formula from the partial specification; if the remainder of the network satisfies this formula, then any process that meets the specification is guaranteed to ensure correct behavior of the overall system. Using the results, the authors develop compositional proof rules for establishing the correctness of networks of parallel processes and illustrate their use with several examples

Guest Editorial. Special Issue: Temporal logic in engineering

Logic-based models are thriving within artificial intelligence. A great number of new logics have been defined, and their theory investigated. Epistemic logics introduce modal operators for knowledge or belief; deontic logics are about norms, and introduce operators of deontic necessity and possibility (i.e., obligation or prohibition). And then we have a much investigated class—temporal logics—to whose application to engineering this special issue is devoted. This kind of formalism deserves increased widespread recognition and application in engineering, a domain where other kinds of temporal models (e.g., Petri nets) are by now a fairly standard part of the modelling toolbox.

Multi-Modal CTL:Completeness, Complexity, and an Application

We define a multi-modal version of Computation Tree Logic (ctl) by extending the language with path quantifiers E and A where d denotes one of finitely many dimensions, interpreted over Kripke structures with one total relation for each dimension. As expected, the logic is axiomatised by taking a copy of a ctl axiomatisation for each dimension. Completeness is proved by employing the completeness result for ctl to obtain a model along each dimension in turn. We also show that the logic is decidable and that its satisfiability problem is no harder than the corresponding problem for ctl. We then demonstrate how Normative Systems can be conceived as a natural interpretation of such a multi-dimensional ctl logic. © 2009 Springer Science+Business Media B.V.

On rich modal logics

I thank to my advisor, João Marcos, for the intellectual support and patience that devoted me along graduate years. With his friendship, his ability to see problems of the better point of view and his love in to make Logic, he became a great inspiration for me. I thank to my committee members: Claudia Nalon, Elaine Pimentel and Benjamin Bedregal. These make a rigorous lecture of my work and give me valuable suggestions to make it better. I am grateful to the Post-Graduate Program in Systems and Computation that accepted me as student and provided to me the propitious environment to develop my research. I thank also to the CAPES for a 21 months fellowship. Thanks to my research group, LoLITA (Logic, Language, Information, Theory and Applications). In this group I have the opportunity to make some friends. Someone of them I knew in my early classes, they are: Sanderson, Haniel and Carol Blasio. Others I knew during the course, among them I’d like to cite: Patrick, Claudio, Flaulles and Ronildo. I thank to Severino Linhares and Maria Linhares who gently hosted me at your home in my first months in Natal. This couple jointly with my colleagues of student flat Fernado, Donátila and Aline are my nuclear family in Natal. I thank my fiancée Luclécia for her precious a ective support and to understand my absence at home during my master. I thank also my parents Manoel and Zenilda, my siblings Alexandre, Paulo and Paula.Without their confidence and encouragement I wouldn’t achieve success in this journey. If you want the hits, be prepared for the misses Carl Yastrzemski