The Experts below are selected from a list of 168 Experts worldwide ranked by ideXlab platform
Lluís Godo - One of the best experts on this subject based on the ideXlab platform.
-
A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables
arXiv: Artificial Intelligence, 2013Co-Authors: Teresa Alsinet, Lluís GodoAbstract:In this paper we present a Propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy Propositional Variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy Propositional Variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.
-
UAI - A Complete Calcultis for Possibilistic Logic Programming with Fuzzy Propositional Variables
2000Co-Authors: Teresa Alsinet, Lluís GodoAbstract:In this paper we present a Propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (ϕ, α), where ϕ is a many valued proposition and α ∈ [0, 1] is a lower bound on the belief on ϕ in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all manyvalued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy Propositional Variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy Propositional Variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.
Dmitry Shkatov - One of the best experts on this subject based on the ideXlab platform.
-
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
Theoretical Aspects of Computing – ICTAC 2018, 2018Co-Authors: Mikhail N. Rybakov, Dmitry ShkatovAbstract:We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single Propositional Variable as they are in the full language, i.e., with an unlimited supply of Propositional Variables. It follows that satisfiability for CTL, as well as for ATL, with a single Variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single Variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one Variable is as hard as satisfiability for arbitrary formulas.
-
SAICSIT - On complexity of Propositional linear-time temporal logic with finitely many Variables
Proceedings of the Annual Conference of the South African Institute of Computer Scientists and Information Technologists, 2018Co-Authors: Mikhail N. Rybakov, Dmitry ShkatovAbstract:It is known [4] that both satisfiability and model-checking problems for Propositional Linear-time Temporal Logic, LTL, with only a single Propositional Variable in the language are PSPACE-complete, which coincides with the complexity of these problems for LTL with an arbitrary number of Propositional Variables [14]. In the present paper, we show that the same result can be obtained by modifying the original proof of PSPACE-hardness for LTL from [14]; i.e., we show how to modify the construction from [14] to model the computations of polynomially-space bound Turing machines using only formulas of one Variable. We believe that our alternative proof of the results from [4] gives additional insight into the semantic and computational properties of LTL.
Shkatov Dmitry - One of the best experts on this subject based on the ideXlab platform.
-
Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables
'Springer Science and Business Media LLC', 2019Co-Authors: Rybakov Mikhail, Shkatov DmitryAbstract:We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single Propositional Variable as they are in the full language, i.e., with an unlimited supply of Propositional Variables. It follows that satisfiability for CTL, as well as for ATL, with a single Variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single Variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one Variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape
-
On complexity of Propositional Linear-time Temporal Logic with finitely many Variables
'Association for Computing Machinery (ACM)', 2018Co-Authors: Rybakov Mikhail, Shkatov DmitryAbstract:It is known [DemriSchnoebelen02] that both satisfiability and model-checking problems for Propositional Linear-time Temporal Logic, LTL, with only a single Propositional Variable in the language are PSPACE-complete, which coincides with the complexity of these problems for LTL with an arbitrary number of Propositional Variables [SislaClarke85]. In the present paper, we show that the same result can be obtained by modifying the original proof of SPACE-hardness for LTL from [SislaClarke85]; i.e., we show how to modify the construction from [SislaClarke85] to model the computations of polynomially-space bound Turing machines using only formulas of one Variable. We believe that our alternative proof of the results from [DemriSchnoebelen02] gives additional insight into the semantic and computational properties of LTL
Yuefei Sui - One of the best experts on this subject based on the ideXlab platform.
-
The Correspondence between Propositional Modal Logic with Axiom $\Box\varphi \leftrightarrow \Diamond \varphi $ and the Propositional Logic
2014Co-Authors: Meiying Sun, Shaobo Deng, Yuefei SuiAbstract:The Propositional modal logic is obtained by adding the necessity operator □ to the Propositional logic. Each formula in the Propositional logic is equivalent to a formula in the disjunctive normal form. In order to obtain the correspondence between the Propositional modal logic and the Propositional logic, we add the axiom $\Box\varphi \leftrightarrow\Diamond\varphi $ to K and get a new system K + . Each formula in such a logic is equivalent to a formula in the disjunctive normal form, where □k(k ≥ 0) only occurs before an atomic formula p, and $\lnot$ only occurs before a pseudo-atomic formula of form □k p. Maximally consistent sets of K + have a property holding in the Propositional logic: a set of pseudo-atom-complete formulas uniquely determines a maximally consistent set. When a pseudo-atomic formula □k pi (k,i ≥ 0) is corresponding to a Propositional Variable qki, each formula in K + then can be corresponding to a formula in the Propositional logic P + . We can also get the correspondence of models between K + and P + . Then we get correspondences of theorems and valid formulas between them. So, the soundness theorem and the completeness theorem of K + follow directly from those of P + .
-
The Correspondence between Propositional Modal Logic with Axiom ϕ ↔ ♦ϕ and the Propositional Logic
2014Co-Authors: Meiying Sun, Shaobo Deng, Yuefei SuiAbstract:The Propositional modal logic is obtained by adding the ne- cessity operatorto the Propositional logic. Each formula in the propo- sitional logic is equivalent to a formula in the disjunctive normal form. In order to obtain the correspondence between the Propositional modal logic and the Propositional logic, we add the axiom � ϕ ↔ ♦ϕ to K and get a new system K + . Each formula in such a logic is equivalent to a for- mula in the disjunctive normal form, wherek (k ≥ 0) only occurs before an atomic formula p ,a nd¬ only occurs before a pseudo-atomic formula of formk p. Maximally consistent sets of K + have a property holding in the Propositional logic: a set of pseudo-atom-complete formulas uniquely determines a maximally consistent set. When a pseudo-atomic formula � k pi(k, i ≥ 0) is corresponding to a Propositional Variable qki, each for- mula in K + then can be corresponding to a formula in the Propositional
-
Intelligent Information Processing - The Correspondence between Propositional Modal Logic with Axiom \Box\varphi \leftrightarrow \Diamond \varphi and the Propositional Logic
Progress in Pattern Recognition Image Analysis Computer Vision and Applications, 2014Co-Authors: Shaobo Deng, Yuefei SuiAbstract:The Propositional modal logic is obtained by adding the necessity operator □ to the Propositional logic. Each formula in the Propositional logic is equivalent to a formula in the disjunctive normal form. In order to obtain the correspondence between the Propositional modal logic and the Propositional logic, we add the axiom \(\Box\varphi \leftrightarrow\Diamond\varphi \) to K and get a new system K + . Each formula in such a logic is equivalent to a formula in the disjunctive normal form, where □ k (k ≥ 0) only occurs before an atomic formula p, and \(\lnot\) only occurs before a pseudo-atomic formula of form □ k p. Maximally consistent sets of K + have a property holding in the Propositional logic: a set of pseudo-atom-complete formulas uniquely determines a maximally consistent set. When a pseudo-atomic formula □ k p i (k,i ≥ 0) is corresponding to a Propositional Variable q ki , each formula in K + then can be corresponding to a formula in the Propositional logic P + . We can also get the correspondence of models between K + and P + . Then we get correspondences of theorems and valid formulas between them. So, the soundness theorem and the completeness theorem of K + follow directly from those of P + .
Teresa Alsinet - One of the best experts on this subject based on the ideXlab platform.
-
A Complete Calculus for Possibilistic Logic Programming with Fuzzy Propositional Variables
arXiv: Artificial Intelligence, 2013Co-Authors: Teresa Alsinet, Lluís GodoAbstract:In this paper we present a Propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (A, c), where A is a many-valued proposition and c is value in the unit interval [0,1] which denotes a lower bound on the belief on A in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all many-valued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy Propositional Variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy Propositional Variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.
-
UAI - A Complete Calcultis for Possibilistic Logic Programming with Fuzzy Propositional Variables
2000Co-Authors: Teresa Alsinet, Lluís GodoAbstract:In this paper we present a Propositional logic programming language for reasoning under possibilistic uncertainty and representing vague knowledge. Formulas are represented by pairs (ϕ, α), where ϕ is a many valued proposition and α ∈ [0, 1] is a lower bound on the belief on ϕ in terms of necessity measures. Belief states are modeled by possibility distributions on the set of all manyvalued interpretations. In this framework, (i) we define a syntax and a semantics of the general underlying uncertainty logic; (ii) we provide a modus ponens-style calculus for a sublanguage of Horn-rules and we prove that it is complete for determining the maximum degree of possibilistic belief with which a fuzzy Propositional Variable can be entailed from a set of formulas; and finally, (iii) we show how the computation of a partial matching between fuzzy Propositional Variables, in terms of necessity measures for fuzzy sets, can be included in our logic programming system.
