First-order Nilpotent Minimum Logics: first steps

Following the lines of the analysis done in [BPZ07, BCF07] for first-order G\"odel logics, we present an analogous investigation for Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra. We establish a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, undecidability and the monadic fragments.Comment: In this version of the paper the presentation has been improved. The introduction section has been rewritten, and many modifications have been done to improve the readability; moreover, numerous references have been added. Concerning the technical side, some proofs has been shortened or made more clear, but the mathematical content is substantially the same of the previous versio

A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

Contributions to artificial intelligence: the IIIA perspective

La intel·ligència artificial (IA) és un camp científic i tecnològic relativament nou dedicat a l'estudi de la intel·ligència mitjançant l'ús d'ordinadors com a eines per produir comportament intel·ligent. Inicialment, l'objectiu era essencialment científic: assolir una millor comprensió de la intel·ligència humana. Aquest objectiu ha estat, i encara és, el dels investigadors en ciència cognitiva. Dissortadament, aquest fascinant però ambiciós objectiu és encara molt lluny de ser assolit i ni tan sols podem dir que ens hi haguem acostat significativament. Afortunadament, però, la IA també persegueix un objectiu més aplicat: construir sistemes que ens resultin útils encara que la intel·ligència artificial de què estiguin dotats no tingui res a veure amb la intel·ligència humana i, per tant, aquests sistemes no ens proporcionarien necessàriament informació útil sobre la naturalesa de la intel·ligència humana. Aquest objectiu, que s'emmarca més aviat dins de l'àmbit de l'enginyeria, és actualment el que predomina entre els investigadors en IA i ja ha donat resultats impresionants, tan teòrics com aplicats, en moltíssims dominis d'aplicació. A més, avui dia, els productes i les aplicacions al voltant de la IA representen un mercat anual de desenes de milers de milions de dòlars. Aquest article resumeix les principals contribucions a la IA fetes pels investigadors de l'Institut d'Investigació en Intel·ligència Artificial del Consell Superior d'Investigacions Científiques durant els darrers cinc anys.Artificial intelligence is a relatively new scientific and technological field which studies the nature of intelligence by using computers to produce intelligent behaviour. Initially, the main goal was a purely scientific one, understanding human intelligence, and this remains the aim of cognitive scientists. Unfortunately, such an ambitious and fascinating goal is not only far from being achieved but has yet to be satisfactorily approached. Fortunately, however, artificial intelligence also has an engineering goal: building systems that are useful to people even if the intelligence of such systems has no relation whatsoever with human intelligence, and therefore being able to build them does not necessarily provide any insight into the nature of human intelligence. This engineering goal has become the predominant one among artificial intelligence researchers and has produced impressive results, ranging from knowledge-based systems to autonomous robots, that have been applied to many different domains. Furthermore, artificial intelligence products and services today represent an annual market of tens of billions of dollars worldwide. This article summarizes the main contributions to the field of artificial intelligence made at the IIIA-CSIC (Artificial Intelligence Research Institute of the Spanish Scientific Research Council) over the last five years

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

This Week's Finds in Mathematical Physics (1-50)

These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993 to March 12, 1995. These issues focus on quantum gravity, topological quantum field theory, knot theory, and applications of $n$-categories to these subjects. However, there are also digressions into Lie algebras, elliptic curves, linear logic and other subjects. They were typeset in 2020 by Tim Hosgood. If you see typos or other problems please report them. (I already know the cover page looks weird).Comment: 242 page