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Canonical Signed Calculi, Nondeterministic Matrices and Cutelimination, forthcoming
 in the Proceedings of LFCS 2009, LNCS
, 2009
"... Abstract. Canonical propositional Gentzentype calculi are a natural class of systems which in addition to the standard axioms and structural rules have only logical rules where exactly one occurrence of a connective is introduced and no other connective is mentioned. Cutelimination in such systems ..."
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in such calculi, while for characterizing strong and standard cutelimination a stronger criterion of density is required. Modular semantics based on nondeterministic matrices are provided for every coherent canonical signed calculus. 1
Strong CutElimination, Coherence, and Nondeterministic Semantics
"... Abstract. An (n, k)ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)ary quantifiers form a natural class of Gentzentype systems which in addition to the standard axioms and structural rules have only logical rules in w ..."
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in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cutelimination, and (iii) G has a strongly characteristic twovalued generalized nondeterministic matrix. In addition, we define simple
CutElimination and Quantification in Canonical Systems
"... Abstract. Canonical propositional Gentzentype systems are systems which in addition to the standard axioms and structural rules have only pure logical rules with the subformula property, in which exactly one occurrence of a connective is introduced in the conclusion, and no other occurrence of any ..."
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. Then we provide semantics for such canonical systems using 2valued nondeterministic matrices extended to languages with quantifiers, and prove that the following properties are equivalent for a canonical system G: (1) G admits CutElimination, (2) G is coherent, and (3) G has a characteristic 2valued
A Triple Correspondence in Canonical Calculi: Strong CutElimination, Coherence, and Nondeterministic Semantics
"... Abstract. An (n, k)ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)ary quantifiers form a natural class of Gentzentype systems which in addition to the standard axioms and structural rules have only logical rules in w ..."
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in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cutelimination, and (iii) G has a strongly characteristic twovalued generalized nondeterministic matrix. 1
Nondeterministic matrices and modular semantics of rules
 in Logica Universalis
, 2005
"... Abstract. We show by way of example how one can provide in a lot of cases simple modular semantics for rules of inference, so that the semantics of a system is obtained by joining the semantics of its rules in the most straightforward way. Our main tool for this task is the use of finite Nmatrices, ..."
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Cited by 27 (11 self)
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, which are multivalued structures in which the value assigned by a valuation to a complex formula can be chosen nondeterministically out of a certain nonempty set of options. The method is applied in the area of logics with a formal consistency operator (known as LFIs), allowing us to provide in a
Towards an Algorithmic Construction of CutElimination Procedures
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2009
"... We investigate cutelimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cutelimination. We show that, for commutative singleconclusion sequent calculi containing generalized knotted structural rules and arbitrary logical rules, the ..."
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Cited by 4 (0 self)
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We investigate cutelimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cutelimination. We show that, for commutative singleconclusion sequent calculi containing generalized knotted structural rules and arbitrary logical rules
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
Results 1  10
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