Automated deduction with built-in theories: completeness results and constraint solving techniques

Postprint (published version

Strategic Issues, Problems and Challenges in Inductive Theorem Proving

Abstract(Automated) Inductive Theorem Proving (ITP) is a challenging field in automated reasoning and theorem proving. Typically, (Automated) Theorem Proving (TP) refers to methods, techniques and tools for automatically proving general (most often first-order) theorems. Nowadays, the field of TP has reached a certain degree of maturity and powerful TP systems are widely available and used. The situation with ITP is strikingly different, in the sense that proving inductive theorems in an essentially automatic way still is a very challenging task, even for the most advanced existing ITP systems. Both in general TP and in ITP, strategies for guiding the proof search process are of fundamental importance, in automated as well as in interactive or mixed settings. In the paper we will analyze and discuss the most important strategic and proof search issues in ITP, compare ITP with TP, and argue why ITP is in a sense much more challenging. More generally, we will systematically isolate, investigate and classify the main problems and challenges in ITP w.r.t. automation, on different levels and from different points of views. Finally, based on this analysis we will present some theses about the state of the art in the field, possible criteria for what could be considered as substantial progress, and promising lines of research for the future, towards (more) automated ITP

Introduction to Milestones in Interactive Theorem Proving

On March 8, 2018, Tobias Nipkow celebrated his sixtieth birthday. In anticipation of the occasion, in January 2016, two of his former students, Gerwin Klein and Jasmin Blanchette, and one of his former postdocs, Andrei Popescu, approached the editorial board of the Journal of Automated Reasoning with a proposal to publish a surprise Festschrift issue in his honor. The e-mail was sent to twenty-six members of the board, leaving out one, for reasons that will become clear in a moment. It is a sign of the love and respect that Tobias commands from his colleagues that within two days every recipient of the e-mail had responded favorably and enthusiastically to the proposal

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

Twenty years of rewriting logic

AbstractRewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. This paper provides a gentle, intuitive introduction to its main ideas, as well as a survey of the work that many researchers have carried out over the last twenty years in advancing: (i) its foundations; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification and verification, security, real-time and cyber-physical systems, probabilistic systems, bioinformatics and chemical systems