Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices, in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the axiom was replaced by the deontic axiom. In this paper, we propose even weaker systems, by eliminating (...) both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

This paper, we propose a modal logic satisfying minimal requirements for reasoning about diagrams via collection of sets and relations between them, following Harel's proposal. We first give an axiomatics of such a theory and then provide its Kripke semantics. Then we extend previous works of ours in order to obtain a decision procedure based on tableaux for this logic. Beside soundness and completeness of our tableaux, we manage to define a strategy of rule application ensuring termination by extending the (...) usual loop test of modal logic S4 to whole sub-structures of the model being computed. (shrink)

Trying to overcome Dugundji’s result on uncharacterisability of modal logics by finite logical matrices, Kearns and Ivlev proposed, independently, a characterisation of some modal systems by means of four-valued multivalued truth-functions , as an alternative to Kripke semantics. This constitutes an antecedent of the non-deterministic matrices introduced by Avron and Lev . In this paper we propose a reconstruction of Kearns’s and Ivlev’s results in a uniform way, obtaining an extension to another modal systems. The first part of the paper (...) is devoted to four-valued Nmatrices, including Kearns’s and Ivlev’s. Besides proving with full details Kearns’s results for T, S4 and S5, we also obtain a characterisation of the system B by four-valued Nmatrices with level valuations. Concerning Ivlev’s results, two new modal systems are introduced and char.. (shrink)

This book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.

ABSTRACT We consider the question of the complete axiomatization of a relative modal logic with composition and intersection.

The primary goal of the present research was to determine the order of swimmers on a mixed relay team that would ensure the best performance in the Fédération Internationale de Natation World Championships held in Kazan, Budapest, and Gwangju. The data were obtained from database websites for the 4 × 100 m freestyle and 4 × 100 m medley official results,1 including 660 records from 188 entries of finals and 472 preliminary events. The results showed that the fastest swimmers were (...) located primarily in the first or second positions of the freestyle relay. The most successful gender strategy for the 4 × 100 m freestyle and for the 4 × 100 m medley relays was the order male-male-female-female, although no statistical differences were found for the medley relays. In the 4 × 100 m freestyle, the second and third relay legs had a statistical effect on the total relay time, whereas in the 4 × 100 m medley, all four relay legs had a statistical effect on the final performance, the weight of the four strokes being different in heats with respect to the final round. Also, a later position of the first female swimmer or the consecutive position of two female swimmers in the team order significantly affected the relay performance in specific events. Mixed relay events appeared to present specific strategies in comparison to traditional male- or female-only relay lineups. (shrink)

ABSTRACT We consider the question of the complete axiomatization of a relative modal logic with composition and intersection.

Internationally recognized logicians present current thinking on the understanding of the role of deduction in human reasoning.

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this paper, we (...) propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

1. A. Heyting (1930) introduced an intermediate logic whose semantics is based on a pair of states (‘here’ and ‘there’). This logic was axiomatized by Hosoi (1966), using the sequence of intermedia...

In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...) in the paper “More modal semantics without possible worlds”, where an alternative solution was proposed. (shrink)

1. Reasoning about action and change, or more generally reasoning about dynamic systems, is not only central to knowledge representation and reasoning but at the heart of computer science (Fisher e...

Psychology research on men studies, attractiveness, and partner preferences has evolved from the influence of sociobiological perspectives to the role of interactions in shaping election toward sexual–affective relationships and desire toward different kinds of masculinities. However, there is a scientific gap in how language and communicative acts among women influence the kind of partner they feel attracted to and in the reproduction of relationship double standards, like the myth of the “warrior’s rest” where female attractiveness to “bad boys” is encouraged (...) or supported. Some women imitate “the warrior” behavior of men by choosing dominant traditional masculinities to have “fun” with and oppressed traditional masculinities for “rest” after the “fun” with DTM—choosing an OTM for a stable relationship, but perhaps without passion, while also feeling attraction toward DTM, a response which perpetuates the chauvinist double standard that the feminist movement has condemned when men behave in this sexist way. Through conducting a qualitative study with communicative daily life stories, this article explores, on the one hand, how language and social interaction among women can lead to the reproduction of the DTM role by women and, on the other hand, also how new alternative masculinities offer an alternative by explicitly rejecting, through the language of desire, to be the rest for the female warrior, the second fiddle to any woman. This has the potential to become a highly attractive alternative to DTM. Findings provide new knowledge through the analysis of communicative acts and masculinities evidencing the importance of language uses in the reproduction of the double standards in gender relations and to understand how and why these practices are maintained and which kind of language uses can contribute to preventing them. Implications for research and interventions on preventive socialization of gender violence are discussed. (shrink)

Near the end of 2015, Luis Fariñas del Cerro officially retired as directeur de recherche in the Centre National de Recherche Scientifique (CNRS) and became an Emeritus researcher of the CNRS. The present special issue is a Festschrift in his honour to celebrate Luis’s achievements in science, both as an outstanding scholar as well as a remarkable and highly successful organiser, administrator and leader in science and technology policy and management, in particular as the founder of (...) the Journal of Applied Non-Classical Logics. The issue contains 13 scientific contributions by 32 authors, among them Luis’s colleagues, former students and friends. Preceding versions of these papers were presented at the international workshop ‘Logical Reasoning and Computation’ that was held at IRITInstitut de Recherche en Informatique de Toulouse, Université Paul Sabatier, Toulouse, on 3–4 March 2016. The present introduction contains a short scientific biography describing the many different areas of logic and computation where Luis contributed significant advances. (shrink)