Nonmonotonic reasoning and nonmonotonic truth maintenance are two important research aspects of artificial intelligence, which have close relations. Existing nonmonotonic truth maintenance systems can be used as the t...Nonmonotonic reasoning and nonmonotonic truth maintenance are two important research aspects of artificial intelligence, which have close relations. Existing nonmonotonic truth maintenance systems can be used as the theorem provers of conventional nonmonotonic logics, but they can't represent and deal with prioritized nonmonotonic reasoning. This paper presented stratified truth maintenance systems which can represent and deal with prioritized justifications. It will be shown that the stratified ATMS can be used as a theorem prover of prioritized nonmonotonic logics.展开更多
Truth maintenance systems become the very useful tools in artificial intelligence. Existing truth maintenance systems can’t deal with nonmonotonic reasoning effectively. They have limitations ...Truth maintenance systems become the very useful tools in artificial intelligence. Existing truth maintenance systems can’t deal with nonmonotonic reasoning effectively. They have limitations in the representation of nonmonotonic justifications. We present stratified truth maintenance systems which introduce priorities among justifications. The stratified truth maintenance systems can deal with nonmonotonic reasoning more effectively and can be applied in many useful areas.展开更多
Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. I...Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.展开更多
This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective functio...This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.展开更多
A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm i...A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.展开更多
The nonmonotonic dose-response curve(NMDRC)is a prevalent characteristic of endocrine-disrupting chemicals(EDCs)in activating nuclear receptors(NRs),implicating intricate regulatory mechanisms.In this study,the agonis...The nonmonotonic dose-response curve(NMDRC)is a prevalent characteristic of endocrine-disrupting chemicals(EDCs)in activating nuclear receptors(NRs),implicating intricate regulatory mechanisms.In this study,the agonistic and antagonistic activities of 11 bisphenols on the estrogen receptor(ER)were screened using MVLN cells.Three distinct dose-response patterns were observed,namely,S-shaped,inverted S-shaped,and bell-shaped profiles,corresponding to the agonistic,antagonistic,and nonmonotonic effects on ERs,respectively.To further explore NMDRC,bisphenol B(BPB)and bisphenol AF(BPAF),as representative compounds,were specifically investigated for their antagonistic effects on ER under high exposure concentrations(10-50μmol/L).Notably,the successive decline in cell viability suggested a subhealthy cell state upon high-dose chemical treatments,compromising cell response in ER transactivation.Unlike the specific effect induced by an ERαantagonist(4-hydroxytamoxifen,4OHT),the nonspecific inhibitory effects of BPB and BPAF on ER transactivation were further confirmed with their identical antagonistic curves,with or without E2 cotreatment,due to hydrophobicity-related cellular baseline toxicity.Accordingly,the inhibitory effects on NR transactivation might not necessarily be considered as a specific antagonistic activity.Thus,a more cautious inspection is highly encouraged in screening NR antagonism-centered endocrine-disrupting effects of emerging chemicals by carefully reviewing the specificity of signal reduction or inhibition.展开更多
In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, ...In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.展开更多
Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which ...Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.展开更多
The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrai...The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.展开更多
This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problem...This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.展开更多
A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the th...A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the theorems relating it to major nonmonotonic logics are proved.It directly formalizes the intuition of nonmonotonic reasoning.Among other things,it provides us a first-order extension of default logic and autoepistemic logic,and simultaneously has the capability of circumscription to infer universal statement.It has important applications in logic programming and deductive data base.As a result,it provides a uniform basis for various nonmonotonic logics,from which the correspondent relationship among major nonmonotonic logics can coincide.展开更多
This paper introduces a non-Horn rule WRM which is a weak form of rational monotony. We explore the effects of adding this non-Horn rule to the rules for the preferential inference. In this paper, a relation |~ is sai...This paper introduces a non-Horn rule WRM which is a weak form of rational monotony. We explore the effects of adding this non-Horn rule to the rules for the preferential inference. In this paper, a relation |~ is said to be P + WRM iff it is a preferential inference and satisfies the rule WRM. We establish the representation theorem for P + WRM, and compare the strength of WRM with some non-Horn rules appearing in literatures. Moreover, we explore the relation between P + WRM and conditional logic, and demonstrate that P + WRM is equivalent to 'flat' fragment of conditional logic CS4.2. Another contribution of this paper is to explore the relation between two special kinds of preferential models, i.e., PRC model and quasi-linear model. Main result reveals that the latter is a special form of the former.展开更多
By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S...By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.展开更多
A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which i...A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. There is a sound, complete and monotonic Gentzen deduction system G for sequents. Dually, there is a sound, complete and nonmonotonic Gentzen deduction system G′ for co-sequents Δ: Θ: Γ. By taking different quantifiers some or every, there are 8 kinds of definitions of validity of multisequent Δ∣Θ∣Γ and 8 kinds of definitions of validity of co-multisequent Δ: Θ: Γ, and correspondingly there are 8 sound and complete Gentzen deduction systems for sequents and 8 sound and complete Gentzen deduction systems for co-sequents. Correspondingly their monotonicity is discussed.展开更多
Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typ...Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typical ones are default logic[2,3],R-calculus[4],autoepistemic logic[5],circumscription[5],etc.展开更多
In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have fi...In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have finitely many fixed points is presented.展开更多
In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumul...In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumulation points of the iterates generated by the proposed algorithm are Kuhn-Tucker points and that the algorithm is q-superlinearly convergent.展开更多
This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to ba...This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.展开更多
Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a m...Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.展开更多
It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre hav...It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre have shown that some conditional implication may b e regarded as the homology of different nonmonotonic consequence relations. In t his paper, based on the plausibility space introduced by Friedman and Halpern, w e characterize the condition logic in which conditional implication is nonmonoto nic, and this result characterizes the conditional implication which may be rega rded as the corresponding object in Meta language for nonmonotonic inference rel ations.展开更多
文摘Nonmonotonic reasoning and nonmonotonic truth maintenance are two important research aspects of artificial intelligence, which have close relations. Existing nonmonotonic truth maintenance systems can be used as the theorem provers of conventional nonmonotonic logics, but they can't represent and deal with prioritized nonmonotonic reasoning. This paper presented stratified truth maintenance systems which can represent and deal with prioritized justifications. It will be shown that the stratified ATMS can be used as a theorem prover of prioritized nonmonotonic logics.
文摘Truth maintenance systems become the very useful tools in artificial intelligence. Existing truth maintenance systems can’t deal with nonmonotonic reasoning effectively. They have limitations in the representation of nonmonotonic justifications. We present stratified truth maintenance systems which introduce priorities among justifications. The stratified truth maintenance systems can deal with nonmonotonic reasoning more effectively and can be applied in many useful areas.
基金the High Technology Research and Development Programme of China
文摘Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.
文摘This paper presents a new trust region algorithm for solving a class of composite nonsmooth optimizations. It is distinguished by the fact that this method does not enforce strict monotonicity of the objective function values at successive iterates and that this method extends the existing results for this type of nonlinear optimization with smooth, or piecewise smooth, or convex objective functions or their composition. It is proved that this algorithm is globally convergent under certain conditions. Finally, some numerical results for several optimization problems are reported which show that the nonmonotonic trust region method is competitive with the usual trust region method.
文摘A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.
基金supported by the National Key R&D Program of China(2024YFA0918800)Strategic Priority Research Program of the Chinese Academy of Sciences(XDB0750300)National Natural Science Foundation of China(22193051,22276212).
文摘The nonmonotonic dose-response curve(NMDRC)is a prevalent characteristic of endocrine-disrupting chemicals(EDCs)in activating nuclear receptors(NRs),implicating intricate regulatory mechanisms.In this study,the agonistic and antagonistic activities of 11 bisphenols on the estrogen receptor(ER)were screened using MVLN cells.Three distinct dose-response patterns were observed,namely,S-shaped,inverted S-shaped,and bell-shaped profiles,corresponding to the agonistic,antagonistic,and nonmonotonic effects on ERs,respectively.To further explore NMDRC,bisphenol B(BPB)and bisphenol AF(BPAF),as representative compounds,were specifically investigated for their antagonistic effects on ER under high exposure concentrations(10-50μmol/L).Notably,the successive decline in cell viability suggested a subhealthy cell state upon high-dose chemical treatments,compromising cell response in ER transactivation.Unlike the specific effect induced by an ERαantagonist(4-hydroxytamoxifen,4OHT),the nonspecific inhibitory effects of BPB and BPAF on ER transactivation were further confirmed with their identical antagonistic curves,with or without E2 cotreatment,due to hydrophobicity-related cellular baseline toxicity.Accordingly,the inhibitory effects on NR transactivation might not necessarily be considered as a specific antagonistic activity.Thus,a more cautious inspection is highly encouraged in screening NR antagonism-centered endocrine-disrupting effects of emerging chemicals by carefully reviewing the specificity of signal reduction or inhibition.
文摘In this paper we modify approximate trust region methods via three precon ditional curvilinear paths for unconstrained optimization. To easily form preconditional curvilinear paths within the trust region subproblem, we employ the stable Bunch-Parlett factorization method of symmetric matrices and use the unit lower triangular matrix as a preconditioner of the optimal path and modified gradient path. In order to accelerate the preconditional conjugate gradient path, we use preconditioner to improve the eigenvalue distribution of Hessian matrix. Based on the trial steps produced by the trust region subproblem along the three curvilinear paths providing a direction of sufficient descent, we mix a strategy using both trust region and nonmonotonic line search techniques which switch to back tracking steps when a trial step is unacceptable. Theoretical analysis is given to prove that the proposed algorithms are globally convergent and have a local su-pcrlinear convergent rate under some reasonable conditions. The results of the numerical experiment are reported to show the effectiveness of the proposed algorithms.
基金the Chinese National Science Foundation Grant 10071050, the Science andTechnology Foundation of Shanghai Higher Education.
文摘Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.
基金the National Natural Science Foundation of China under Grant No.10471094the Ph.D.Foundation under Grant No.0527003+1 种基金the Shanghai Leading Academic Discipline Project (T0401)the Science Foundation of Shanghai Education Committee under Grant No.05DZ11
文摘The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.
基金The author gratefully acknowledges the partial supports of the National Science Foundation of China Grant (10071050)Science Foundation of Shanghai Technical Sciences Committee Grant (02ZA14070) Science Foundation of Shanghai Education Committee Grant
文摘This paper proposes a two-piece update of projected reduced Hessian algorithmwith nonmonotonic trust region strategy for solving nonlinear equality constrained optimizationproblems. In order to deal with large problems, a two-piece update of two-side projected reducedHessian is used to replace full Hessian matrix. By adopting the Fletcher's penalty function as themerit function, a nonmonotonic trust region strategy is suggested which does not require the meritfunction to reduce its value in every iteration. The two-piece update of projected reduced Hessianalgorithm which switches to nonmonotonic trust region technique possesses global convergence whilemaintaining a two-step Q-superlinear local convergence rate under some reasonable conditions.Furthermore, one step Q-superlinear local convergence rate can be obtained if at least one of theupdate formulas is updated at each iteration by an alternative update rule. The numerical experimentresults are reported to show the effectiveness of the proposed algorithm.
基金Project in part supported by the National Natural Science Foundation of China, the National Hi-Tech 863 Programme, the National Project of Fundamental Research (Climbing)and by Guangdong Natural Science Foundation.
文摘A modal nonmonotonic logic is presented based on an experiential modal semantics on typicality and exception.The syntactic and semantics of modal nonmonotonic logic are provided,and the completeness theorem and the theorems relating it to major nonmonotonic logics are proved.It directly formalizes the intuition of nonmonotonic reasoning.Among other things,it provides us a first-order extension of default logic and autoepistemic logic,and simultaneously has the capability of circumscription to infer universal statement.It has important applications in logic programming and deductive data base.As a result,it provides a uniform basis for various nonmonotonic logics,from which the correspondent relationship among major nonmonotonic logics can coincide.
基金the National Natural Science Foundation of China (No.69875007) and the Science Foundation of Jiangsu Province (No.BK99119).
文摘This paper introduces a non-Horn rule WRM which is a weak form of rational monotony. We explore the effects of adding this non-Horn rule to the rules for the preferential inference. In this paper, a relation |~ is said to be P + WRM iff it is a preferential inference and satisfies the rule WRM. We establish the representation theorem for P + WRM, and compare the strength of WRM with some non-Horn rules appearing in literatures. Moreover, we explore the relation between P + WRM and conditional logic, and demonstrate that P + WRM is equivalent to 'flat' fragment of conditional logic CS4.2. Another contribution of this paper is to explore the relation between two special kinds of preferential models, i.e., PRC model and quasi-linear model. Main result reveals that the latter is a special form of the former.
文摘By L. we denote the set of all propositional fornmlas. Let C be the set of all clauses. Define C_n=C(Lη:η∈C}.In Sec. 2 of this paper. we prove that for normal modal logics S, the notions of (S. C_)-expansions and S-expansions coincide. In Sec. 3. we prove that if I consists of default clauses then the notions of S-expansions for I and (S.C)-expansions for I coincide. To this end. we first show. in Sec 3.that the notion of S-expansions for I is the same as that of (S.L)-expansions for I.
基金supported by the Open Fund of the State KeyLaboratory of Sofware Development Environment(SKLSDE-2010KF-06)Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901).
文摘A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L_(3)-valued propositional logic, a multisequent is a triple Δ∣Θ∣Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. There is a sound, complete and monotonic Gentzen deduction system G for sequents. Dually, there is a sound, complete and nonmonotonic Gentzen deduction system G′ for co-sequents Δ: Θ: Γ. By taking different quantifiers some or every, there are 8 kinds of definitions of validity of multisequent Δ∣Θ∣Γ and 8 kinds of definitions of validity of co-multisequent Δ: Θ: Γ, and correspondingly there are 8 sound and complete Gentzen deduction systems for sequents and 8 sound and complete Gentzen deduction systems for co-sequents. Correspondingly their monotonicity is discussed.
基金supported by the Open Fund of the State Key Laboratory of Software Development Environment(SKLSDE-2010KF-06)Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901)。
文摘Propositional logic[1]is basic,based on which other logics are developed.The deduction system for propositional logic is monotonic.Nonmonotonic logics are a class of logics which deduction systems are nonmonotonic.Typical ones are default logic[2,3],R-calculus[4],autoepistemic logic[5],circumscription[5],etc.
文摘In this paper,a topological classification of piecewise monotone functions(abbreviated as PM functions)with nonmonotonicity height equal to 1 which are strictly increasing on their characteristic intervals and have finitely many fixed points is presented.
文摘In this paper, a nonmonotonic trust region method for optimization problems with equality constraints is proposed by introducing a nonsmooth merit function and adopting a correction step. It is proved that all accumulation points of the iterates generated by the proposed algorithm are Kuhn-Tucker points and that the algorithm is q-superlinearly convergent.
文摘This paper proposes projected gradient algorithms in association with using both trust region and line search techniques for convex constrained optimization problems. The mixed strategy is adopted which switches to back tracking steps when a trial projected gradient step produced by the trust region subproblem is unacceptable. A nonmonotone criterion is used to speed up the convergence progress in some curves with large curvature. A theoretical analysis is given which proves that the proposed algorithms are globally convergent and have local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithms.
文摘Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.
文摘It is well known that there exists a tight connection between nonmonotonic reasoning and conditional implication. Many researchers have investigated it from various angles. Among th em, C.Boutilier and P.Lamarre have shown that some conditional implication may b e regarded as the homology of different nonmonotonic consequence relations. In t his paper, based on the plausibility space introduced by Friedman and Halpern, w e characterize the condition logic in which conditional implication is nonmonoto nic, and this result characterizes the conditional implication which may be rega rded as the corresponding object in Meta language for nonmonotonic inference rel ations.
