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Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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Cited by 45 (7 self)
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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Cited by 45 (19 self)
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
The Power of Vacillation in Language Learning
, 1992
"... Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are ..."
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Cited by 44 (11 self)
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Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are classes of languages that can be learned if convergence in the limit to up to (n+1) exactly correct grammars is allowed but which cannot be learned if convergence in the limit is to no more than n grammars, where the no more than n grammars can each make finitely many mistakes. This contrasts sharply with results of Barzdin and Podnieks and, later, Case and Smith, for learnability from both positive and negative data. A subset principle from a 1980 paper of Angluin is extended to the vacillatory and other criteria of this paper. This principle, provides a necessary condition for circumventing overgeneralization in learning from positive data. It is applied to prove another theorem to the eff...
Toward an MT system without preediting – effects of new methods in ALTJ/E
 In Proc. of the Third Machine Translation Summit (MT Summit III
, 1991
"... Recently, several types of JapanesetoEnglish machine translation systems have been developed, but all of them require an initial process of rewriting the original text into easily translatable Japanese. Therefore these systems are unsuitable for translating information that needs to be speedily di ..."
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Cited by 39 (7 self)
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Recently, several types of JapanesetoEnglish machine translation systems have been developed, but all of them require an initial process of rewriting the original text into easily translatable Japanese. Therefore these systems are unsuitable for translating information that needs to be speedily disseminated. To overcome this limitation, a MultiLevel Translation Method based on the Constructive Process Theory has been proposed. This paper describes the benefits of using this method in the JapanesetoEnglish machine translation system ALTJ/E. In comparison with conventional compositional methods, the MultiLevel Translation Method emphasizes the importance of the meaning contained in expression structures as a whole. It is shown to be capable of translating typical written Japanese based on the meaning of the text in its context, with comparative ease. We are now hopeful of carrying out useful machine translation with no manual preediting. 1
An observationally complete program logic for imperative higherorder functions
 In Proc. LICS’05
, 2005
"... Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of comple ..."
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Cited by 39 (11 self)
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Abstract. We propose a simple compositional program logic for an imperative extension of callbyvalue PCF, built on Hoare logic and our preceding work on program logics for pure higherorder functions. A systematic use of names and operations on them allows precise and general description of complex higherorder imperative behaviour. The proof rules of the logic exactly follow the syntax of the language and can cleanly embed, justify and extend the standard proof rules for total correctness of Hoare logic. The logic offers a foundation for general treatment of aliasing and local state on its basis, with minimal extensions. After establishing soundness, we prove that valid assertions for programs completely characterise their behaviour up to observational congruence, which is proved using a variant of finite canonical forms. The use of the logic is illustrated through reasoning examples which are hard to assert and infer using existing program logics.
Robust Semantics for Argumentation Frameworks
 Journal of Logic and Computation
, 1999
"... We suggest a socalled "robust" semantics for a model of argumentation which represents arguments and their interactions, called "argumentation frameworks". We study a variety of additional definitions of acceptability of arguments; we explore the properties of these definitions; we describe their i ..."
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Cited by 38 (1 self)
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We suggest a socalled "robust" semantics for a model of argumentation which represents arguments and their interactions, called "argumentation frameworks". We study a variety of additional definitions of acceptability of arguments; we explore the properties of these definitions; we describe their interrelationships: e.g. robust models can be characterized using the minimal (wellfounded) models of a metaframework. The various definitions of acceptability of argument sets can all deal with contradiction within an argumentation framework. Keywords: Argumentation framework, semantics 1 Introduction In this paper we present semantics for a formal model of argumentation. As in other works such as [Pol94] and [Dun95], we abstract from the actual contents and form of the arguments themselves, and rather concentrate on the analysis of interactions between arguments. Argumentationtheoretic interpretations and proofprocedures are applicable in practical reasoning, legal reasoning ([KT96]...
C.: The SMTLIB Standard: Version 2.0
, 2010
"... Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified ver ..."
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Cited by 37 (2 self)
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Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified versions may not be made. Preface The SMTLIB initiative is an international effort, supported by several research groups worldwide, with the twofold goal of producing an extensive online library of benchmarks and promoting the adoption of common languages and interfaces for SMT solvers. This document specifies Version 2.0 of the SMTLIB Standard. This is a major upgrade of the previous version, Version 1.2, which, in addition to simplifying and extending the languages of that version, includes a new command language for interfacing with SMT solvers. Acknowledgments Version 2.0 of the SMTLIB standard was developed with the input of the whole SMT community and three international work groups consisting of developers and users of SMT tools: the SMTAPI work group, led by A. Stump, the SMTLOGIC work group, led by C. Tinelli, the SMTMODELS work group, led by C. Barrett. Particular thanks are due to the following work group members, who contributed numerous
Active Logics: A Unified Formal Approach to Episodic Reasoning
"... Artificial intelligence research falls roughly into two categories: formal and implementational. This division is not completely firm: there are implementational studies based on (formal or informal) theories (e.g., CYC, SOAR, OSCAR), and there are theories framed with an eye toward implementabili ..."
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Cited by 35 (2 self)
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Artificial intelligence research falls roughly into two categories: formal and implementational. This division is not completely firm: there are implementational studies based on (formal or informal) theories (e.g., CYC, SOAR, OSCAR), and there are theories framed with an eye toward implementability (e.g., predicate circumscription). Nevertheless, formal /theoretical work tends to focus on very narrow problems (and even on very special cases of very narrow problems) while trying to get them "right" in a very strict sense, while implementational work tends to aim at fairly broad ranges of behavior but often at the expense of any kind of overall conceptually unifying framework that informs understanding. It is sometimes urged that this gap is intrinsic to the topic: intelligence is not a unitary thing for which there will be a unifying theory, but rather a "society" of subintelligences whose overall behavior cannot be reduced to useful characterizing and predictive principles.
Ontologies for Plane, Polygonal Mereotopology
, 1997
"... Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotop ..."
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Cited by 31 (3 self)
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Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in 2dimensional space. Our strategy is to define a mereotopological language together with a familiar, pointbased interpretation. It is proposed that, to be practically useful, any alternative regionbased spatial ontology must support the same sentences in our language as this familiar interpretation. This proposal has the merit of transforming a vague, openended question about ontologies for "practical" mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace.
Planning in Polynomial Time: The SASPUBS Class
 Computational Intelligence
, 1991
"... This article describes a polynomialtime, O(n³), planning algorithm for a limited class of planning problems. Compared to previous work on complexity of algorithms for knowledgebased or logicbased planning, our algorithm achieves computational tractability, but at the expense of only applying ..."
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Cited by 30 (14 self)
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This article describes a polynomialtime, O(n³), planning algorithm for a limited class of planning problems. Compared to previous work on complexity of algorithms for knowledgebased or logicbased planning, our algorithm achieves computational tractability, but at the expense of only applying to a significantly more limited class of problems. Our algorithm is proven correct, and it always returns a parallel minimal plan if there is a plan at all.