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36
On the issue of reinstatement in argumentation
, 2006
"... Abstract. Dung’s theory of abstract argumentation frameworks [1] led to the formalization of various argumentbased semantics, which are actually particular forms of dealing with the issue of reinstatement. In this paper, we reexamine the issue of semantics from the perspective of postulates. In pa ..."
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Cited by 51 (13 self)
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Abstract. Dung’s theory of abstract argumentation frameworks [1] led to the formalization of various argumentbased semantics, which are actually particular forms of dealing with the issue of reinstatement. In this paper, we reexamine the issue of semantics from the perspective of postulates. In particular, we ask ourselves the question of which (minimal) requirements have to be fulfilled by any principle for handling reinstatement, and how this relates to Dung’s standard semantics. Our purpose is to shed new light on the ongoing discussion on which semantics is most appropriate. 1
Canonical Propositional GentzenType Systems
 in Proceedings of the 1st International Joint Conference on Automated Reasoning (IJCAR 2001) (R. Goré, A Leitsch, T. Nipkow, Eds), LNAI 2083
, 2001
"... . Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connectiv ..."
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Cited by 29 (16 self)
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. Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules which have the subformula property, introduce exactly one occurrence of a connective in their conclusion, and no other occurrence of any connective is mentioned anywhere else in their formulation. We provide a constructive coherence criterion for the nontriviality of such systems, and show that a system of this kind admits cut elimination i it is coherent. We show also that the semantics of such systems is provided by nondeterministic twovalued matrices (2Nmatrices). 2Nmatrices form a natural generalization of the classical twovalued matrix, and every coherent canonical system is sound and complete for one of them. Conversely, with any 2Nmatrix it is possible to associate a coherent canonical Gentzentype system which has for each connective at most one introduction rule for each side, and is sound and complete for th...
Sequent and Hypersequent Calculi for Abelian and Łukasiewicz Logics
 ACM Transactions on Computational Logic
, 2005
"... We present two embeddings of infinitevalued ̷Lukasiewicz logic ̷L into Meyer and Slaney’s abelian logic A, the logic of latticeordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for ̷L. These include: hypersequent calculi for A a ..."
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Cited by 19 (6 self)
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We present two embeddings of infinitevalued ̷Lukasiewicz logic ̷L into Meyer and Slaney’s abelian logic A, the logic of latticeordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for ̷L. These include: hypersequent calculi for A and ̷L and terminating versions of these calculi; labelled single sequent calculi for A and ̷L of complexity coNP; unlabelled single sequent calculi for A and ̷L. 1
Quantified Constraints under Perturbation
 ARTICLE SUBMITTED TO JOURNAL OF SYMBOLIC COMPUTATION
"... Quantified constraints (i.e., firstorder formulae over the real numbers) are often exposed to perturbations: Constants that come from measurements usually are only known up to certain precision, and numerical methods only compute with approximations of real numbers. In this paper we study the be ..."
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Cited by 16 (11 self)
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Quantified constraints (i.e., firstorder formulae over the real numbers) are often exposed to perturbations: Constants that come from measurements usually are only known up to certain precision, and numerical methods only compute with approximations of real numbers. In this paper we study the behavior of quantified constraints under perturbation by showing that one can formulate the problem of solving quantified constraints as a nested parametric optimization problem followed by one sign computation. Using the fact that minima and maxima are stable under perturbation, but the sign of a real number is stable only for nonzero inputs, we derive practically useful conditions for the stability of quantified constraints under perturbation.
Hypersequent calculi for Gödel logics: a survey
 Journal of Logic and Computation
, 2003
"... Hypersequent calculi arise by generalizing standard sequent calculi to refer to whole contexts of sequents instead of single sequents. We present a number of results using hypersequents to obtain a Gentzenstyle characterization for the family of Gödel logics. We first describe analytic calculi for ..."
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Cited by 13 (4 self)
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Hypersequent calculi arise by generalizing standard sequent calculi to refer to whole contexts of sequents instead of single sequents. We present a number of results using hypersequents to obtain a Gentzenstyle characterization for the family of Gödel logics. We first describe analytic calculi for propositional finite and infinitevalued Gödel logics. We then show that the framework of hypersequents allows one to move straightforwardly from the propositional level to firstorder as well as propositional quantification. A certain type of modalities, enhancing the expressive power of Gödel logic, is also considered. 1
Logical Nondeterminism as a Tool for Logical Modularity: An Introduction
 in We Will Show Them: Essays in Honor of Dov Gabbay, Vol
, 2005
"... It is well known that every propositional logic which satisfies certain very ..."
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Cited by 13 (10 self)
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It is well known that every propositional logic which satisfies certain very
General logics
 In Logic Colloquium 87
, 1989
"... theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms repre ..."
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Cited by 9 (3 self)
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theory, categorical logic. model theory that emerged in computer science studies of software specification and semantics. To handle proof theory, our institutions use an extension of traditional categorical logic with sets of sentences as objects instead of single sentences, and with morphisms representing proofs as usual. A natural equivalence relation on institutions is defined such that its equivalence classes are logics. Several invariants are defined for this equivalence, including a Lindenbaum
Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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Cited by 8 (1 self)
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
The Role(s) of Logic in Artificial Intelligence
 Handbook of Logic in Artificial Intelligence and Logic Programming
, 1993
"... this paper has been made possible by a gift from the System Development Foundation and was conducted as part of a coordinated research effort with the Center for the Study of Language and Information, Stanford University 30 References ..."
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Cited by 7 (0 self)
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this paper has been made possible by a gift from the System Development Foundation and was conducted as part of a coordinated research effort with the Center for the Study of Language and Information, Stanford University 30 References
On Urquhart's C Logic
 In International Symposium on Multiple Valued Logic (ISMVL’2000
, 2000
"... In this paper we investigate the basic manyvalued logics introduced by Urquhart in [15] and [16], here referred to as C and Cnew , respectively. We define a cutfree hypersequent calculus for Cnew and show the following results: (1) C and Cnew are distinct versions of G odel logic without contracti ..."
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Cited by 5 (2 self)
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In this paper we investigate the basic manyvalued logics introduced by Urquhart in [15] and [16], here referred to as C and Cnew , respectively. We define a cutfree hypersequent calculus for Cnew and show the following results: (1) C and Cnew are distinct versions of G odel logic without contraction. (2) Cnew is decidable. (3) In Cnew the family of axioms ((A k ! C) ^ (B k ! C)) ! ((A _ B) k ! C), with k 2, is in fact redundant. 1 Introduction The logic C was introduced by Urquhart in the chapter devoted to manyvalued logic of the Handbook of Philosophical Logic [15]. C turns out to be a basic manyvalued logic being contained in the most important formalizations of fuzzy logic [7], namely infinitevalued Godel, L/ukasiewicz and product logic (see [3]). In [9, 10] C was shown to be a particular Godel logic without contraction. A cutfree calculus for C was defined in [3]. This calculus uses hypersequents that are a natural generalization of Gentzen sequents. Due to sema...