Fiftieth volume of theoretical computer science
TL;DR: This contribution was made possible only by the miraculous fact that the first members of the Editorial Board were sharing the same conviction about the necessity of Theoretical Computer Science.
Abstract: The collection of TCS issues is about 1 meter high, 17,000 pages long and it contains 1100 papers. When in 1974 Einar Fredriksson and myself started talking about the creation of a journal dedicated to Theoretical Computer Science we were very far from even dreaming that it could take such an extension within twelve years. We were also a bit shy: what could such a journal, very theoretical indeed and hard to read, be useful to, and who would read it? Fortunately, some people encouraged us and indeed helped us a lot, Mike Paterson who was at that time President of EATCS and who accepted to become Associate Editor, Albert Meyer who was a very active editor at the beginning, Arto Salomaa, who was to become President of EATCS shortly afterwards. Indeed, I should mention all the first members of the Editorial Board, for TCS would never have come to existence without them. Theoretical Computer Science is not a clearly defined discipline with neat borderlines: it is more a state of mind, the conviction that the observed computation phenomena can be formally described and analysed as any physical phenomenon; the conviction that such a formal description helps to understand these phenomena and to master them in order to design better algorithms, better computers, better systems. Our fundamental activity is not to prove theorems in strange mathematical theories, it is to model a complicated reality and in this respect it has to be compared with theoretical physics or what we call in French “Mecanique rationnelle”. This comparison can be pursued rather far, for we also use all possible mathematical concepts and methods and when we do not find appropriate ones in traditional mathematics we create them. The aim is quite clear: using the compact and unambiguous language of mathematics brings to life concepts and methods which will be useful to all designers, builders and users of computer systems, exactly in the same way as matrix calculus or Fourier series and transforms are useful to all engineers and technicians in the electric and electronic industry. And when one thinks about the amount of time it took to build the mathematical theory of matrices and to polish and simplify it up to the state in which it could be taught to all future engineers and become a tool in daily use, we can be extremely satisfied by the development of Theoretical Computer Science. It is true that concepts and methods which were still vague and unclear when TCS was created became essential tools for all industrial designers and manufacturers, in algorithmics, in semantics, in automata theory and control, etc. . . . Certainly, TCS can be proud to have contributed to this development. Coming back to what I was saying a few minutes ago, this contribution was made possible only by the miraculous fact that the first members of the Editorial Board were sharing the same conviction about the necessity of Theoretical Computer Science
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TL;DR: This paper investigates a weaker logic, MTL, which is intended to cope with the tautologies of left-continuous t-norms and their residua, and completeness of MTL with respect to linearly ordered MTL-algebras is proved.
Abstract: Hajek's BL logic is the fuzzy logic capturing the tautologies of continuous t-norms and their residua. In this paper we investigate a weaker logic, MTL, which is intended to cope with the tautologies of left-continuous t-norms and their residua. The corresponding algebraic structures, MTL-algebras, are defined and completeness of MTL with respect to linearly ordered MTL-algebras is proved. Besides, several schematic extensions of MTL are also considered as well as their corresponding predicate calculi.
900 citations
TL;DR: In this article, a reference guide to various notions of monoidal categories and their associated string diagrams is presented, which is useful not only to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning.
Abstract: This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning We have opted for a somewhat informal treatment of topological notions, and have omitted most proofs Nevertheless, the exposition is sufficiently detailed to make it clear what is presently known, and to serve as a starting place for more in-depth study Where possible, we provide pointers to more rigorous treatments in the literature Where we include results that have only been proved in special cases, we indicate this in the form of caveats
732 citations
TL;DR: This paper shows how a resource-oriented logic, separation logic, can be used to reason about the usage of resources in concurrent programs.
Abstract: In this paper we show how a resource-oriented logic, separation logic, can be used to reason about the usage of resources in concurrent programs.
560 citations
TL;DR: This paper presents a computational study of part of the lexical-acquisition task faced by children, namely the acquisition of word-to-meaning mappings, and presents an implemented algorithm for solving this problem, illustrating its operation on a small example.
Abstract: This paper presents a computational study of part of the lexical-acquisition task faced by children, namely the acquisition of word-to-meaning mappings. It first approximates this task as a formal mathematical problem. It then presents an implemented algorithm for solving this problem, illustrating its operation on a small example. This algorithm offers one precise interpretation of the intuitive notions of cross-situational learning and the principle of contrast applied between words in an utterance. It robustly learns a homonymous lexicon despite noisy multi-word input, in the presence of referential uncertainty, with no prior knowledge that is specific to the language being learned. Computational simulations demonstrate the robustness of this algorithm and illustrate how algorithms based on cross-situational learning and the principle of contrast might be able to solve lexical-acquisition problems of the size faced by children, under weak, worst-case assumptions about the type and quantity of data available.
524 citations
01 Jan 1997
TL;DR: Categorial type logics developed out of the Syntactic Calculus proposed by Lambek fifty years ago, and complemented in the 1980'ies with a ‘proofs-as-programs’ interpretation associating derivations in a syntactic source calculus with terms of the simply typed linear lambda calculus expressing meaning composition.
Abstract: Categorial type logics developed out of the Syntactic Calculus proposed by Lambek fifty years ago, and complemented in the 1980'ies with a ‘proofs-as-programs’ interpretation associating derivations in a syntactic source calculus with terms of the simply typed linear lambda calculus expressing meaning composition.
503 citations