Results 1 - 10 of 161

Non-Deterministic Matrices

by Arnon Avron And, Arnon Avron, Iddo Lev - in Proceedings of the 34th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2004), 282-287, IEEE Computer , 2000
"... We generalize the ordinary concept of a matrix by introducing non-deterministic matrices (N-matrices). We show that some important logics for reasoning under uncertainty can be characterized by nite N-matrices (and so they are decidable) although they have only innite characteristic matrices. We pro ..."
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We generalize the ordinary concept of a matrix by introducing non-deterministic matrices (N-matrices). We show that some important logics for reasoning under uncertainty can be characterized by nite N-matrices (and so they are decidable) although they have only innite characteristic matrices. We

Non-deterministic matrices and modular semantics of rules

by Arnon Avron - 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, ..."
Abstract - Cited by 27 (11 self) - Add to MetaCart
, which are multi-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically 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

Canonical Signed Calculi, Non-deterministic Matrices and Cut-elimination, forthcoming

by Arnon Avron, Anna Zamansky - in the Proceedings of LFCS 2009, LNCS , 2009
"... Abstract. Canonical propositional Gentzen-type 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. Cut-elimination in such systems ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
-elimination in such calculi, while for characterizing strong and standard cut-elimination a stronger criterion of density is required. Modular se-mantics based on non-deterministic matrices are provided for every co-herent canonical signed calculus. 1

Distance-Based Non-Deterministic Semantics

by Ofer Arieli A, Anna Zamansky B
"... Abstract. Representing uncertainty and reasoning with dynamically evolving systems are two related issues that are in the heart of many information systems. In this paper we show that these tasks can be successfully dealt with by incorporating distance semantics and non-deterministic matrices. The o ..."
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Abstract. Representing uncertainty and reasoning with dynamically evolving systems are two related issues that are in the heart of many information systems. In this paper we show that these tasks can be successfully dealt with by incorporating distance semantics and non-deterministic matrices

Effective Non-deterministic Semantics for first-order LFIs

by Arnon Avron, Anna Zamansky
"... A paraconsistent logic is a logic which allows non-trivial inconsistent theories. One of the best-known approaches to designing useful paraconsistent logics is da Costa’s approach, which has led to the family of Logics of Formal Inconsistency (LFIs), where the notion of inconsistency is expressed at ..."
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at the object level. In this paper we use non-deterministic matrices, a generalization of standard multi-valued matrices, to provide simple and modular finite-valued semantics for a large family of first-order LFIs. We demonstrate that the modular approach of Nmatrices provides new insights into the semantic

Distance-based non-deterministic semantics for reasoning with uncertainty. Logic

by Ofer Arieli, Anna Zamansky - Handbook of Mathematical Logic , 2009
"... Abstract. Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance-based co ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Abstract. Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining non-deterministic matrices and distance

Non-deterministic Multivalued Matrices for First-order Logics of Formal Inconsistency

by Arnon Avron, Anna Zamansky - Proceedings of the 37th IEEE International Symposium on Multiple-Valued Logics , 2007
"... Paraconsistent logic is the study of contradictory yet non-trivial theories. One of the best-known approaches to designing useful paraconsistent logics is da Costa’s ap-proach, which has led to the family of Logics of Formal Inconsistency (LFIs), where the notion of inconsistency is expressed at the ..."
Abstract - Cited by 1 (1 self) - Add to MetaCart
at the object level. In this paper we use non-deterministic matrices, a generalization of standard multi-valued matrices, to provide simple and modular finite-valued semantics for a large family of first-order LFIs. The modular approach provides new insights into the semantic role of each of the studied axioms

Strong Cut-Elimination, Coherence, and Non-deterministic Semantics

by Arnon Avron, Anna Zamansky , 2007
"... 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 Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exac ..."
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exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut

A Triple Correspondence in Canonical Calculi: Strong Cut-Elimination, Coherence, and Non-deterministic Semantics

by Arnon Avron, Anna Zamansky
"... 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 Gentzen-type systems which in addition to the standard axioms and structural rules have only logical rules in which exa ..."
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exactly one occurrence of a quantifier is introduced. The semantics for these systems is provided using two-valued non-deterministic matrices, a generalization of the classical matrix. In this paper we use a constructive syntactic criterion of coherence to characterize strong cut

Reasoning with Uncertainty by Nmatrix–Metric Semantics

by Ofer Arieli, Anna Zamansky
"... Abstract. Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining Nmatrices and preferential metrics-based conside ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
Abstract. Non-deterministic matrices, a natural generalization of many-valued matrices, are semantic structures in which the value assigned to a complex formula may be chosen non-deterministically from a given set of options. We show that by combining Nmatrices and preferential metrics
Results 1 - 10 of 161