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Journal articles on the topic 'Propositional resolution'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 January 2023

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1

PLAZA, JAN A. "ON THE PROPOSITIONAL SLDNF-RESOLUTION." International Journal of Foundations of Computer Science 07, no. 04 (December 1996): 359–406. http://dx.doi.org/10.1142/s0129054196000269.

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We consider propositional logic programs with negations. We define notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued fix-point or declarative semantics for program P are equivalent to the two-valued semantics for the constructive version of P. We argue that it would be beneficial to replace Negation as Failure by constructive transformation, and it would be beneficial to use the semantics for the constructive version of the program instead of multivalued semantics for the original program.

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2

UZQUIANO, GABRIEL. "A NEGLECTED RESOLUTION OF RUSSELL’S PARADOX OF PROPOSITIONS." Review of Symbolic Logic 8, no. 2 (March 31, 2015): 328–44. http://dx.doi.org/10.1017/s1755020315000106.

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AbstractBertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell’s paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some of the uses to which modern descendants of Russell’s paradox of propositions have been put in recent literature.

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3

Auffray, Yves. "Linear strategy for propositional modal resolution." Information Processing Letters 28, no. 2 (June 1988): 87–92. http://dx.doi.org/10.1016/0020-0190(88)90169-x.

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4

MAREK, V. W., and J. B. REMMEL. "Guarded resolution for Answer Set Programming." Theory and Practice of Logic Programming 11, no. 1 (March 24, 2010): 111–23. http://dx.doi.org/10.1017/s1471068410000062.

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AbstractWe investigate a proof system based on a guarded resolution rule and show its adequacy for the stable semantics of normal logic programs. As a consequence, we show that Gelfond–Lifschitz operator can be viewed as a proof-theoretic concept. As an application, we find a propositional theory EP whose models are precisely stable models of programs. We also find a class of propositional theories 𝓒P with the following properties. Propositional models of theories in 𝓒P are precisely stable models of P, and the theories in 𝓒T are of the size linear in the size of P.

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5

Van Gelder, Allen. "Complexity analysis of propositional resolution with autarky pruning." Discrete Applied Mathematics 96-97 (October 1999): 195–221. http://dx.doi.org/10.1016/s0166-218x(99)00040-2.

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6

Stachniak, Zbigniew. "Minimization of Resolution Proof Systems." Fundamenta Informaticae 14, no. 1 (January 1, 1991): 129–46. http://dx.doi.org/10.3233/fi-1991-14107.

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In this paper we show that minimal resolution counterparts of strongly finite logics can be effectively constructed. Moreover, we show that the class of resolution counterparts of structural propositional logics coincides with the class of resolution counterparts of strongly finite logics.

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7

Walicki, Michal, and Sjur Dyrkolbotn. "Paraconsistent resolution." Australasian Journal of Logic 19, no. 3 (September 6, 2022): 96–123. http://dx.doi.org/10.26686/ajl.v19i3.6471.

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Digraphs provide an alternative syntax for propositional logic, with digraph kernels corresponding to classical models. Semikernels generalize kernels and we identify a subset of well-behaved semikernels that provides nontrivial models for inconsistent theories, specializing to the classical semantics for the consistent ones. Direct (instead of refutational) reasoning with classical resolution is sound and complete for this semantics, when augmented with a specific weakening which, in particular, excludes Ex Falso. Dropping all forms of weakening yields reasoning which also avoids typical fallacies of relevance.

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LIMA, PRISCILA M. V. "A GOAL-DRIVEN NEURAL PROPOSITIONAL INTERPRETER." International Journal of Neural Systems 11, no. 03 (June 2001): 311–22. http://dx.doi.org/10.1142/s012906570100076x.

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This work presents ARQ-PROP-II, the propositional version of a neural engine for finding proofs by refutation using the Resolution Principle. This neural architecture does not require special arrangements or modules to do forward or backward reasoning, being driven by the goal posed to it. ARQ-PROP-II is capable of integrated monotonic reasoning with complete and incomplete knowledge. The neural mechanism presented herein is the first to our knowledge that does not require that the knowledge base be either pre-encoded or learnt.

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9

Buss, Samuel R. "Polynomial size proofs of the propositional pigeonhole principle." Journal of Symbolic Logic 52, no. 4 (December 1987): 916–27. http://dx.doi.org/10.2307/2273826.

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AbstractCook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounded arithmetic.

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10

Zou, Li, XiaoNan Li, Chang Pan, and Xin Liu. "( α, β )-Ordered linear resolution of intuitionistic fuzzy propositional logic." Information Sciences 414 (November 2017): 329–39. http://dx.doi.org/10.1016/j.ins.2017.05.046.

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11

Atserias, Albert, and Marı́a Luisa Bonet. "On the automatizability of resolution and related propositional proof systems." Information and Computation 189, no. 2 (March 2004): 182–201. http://dx.doi.org/10.1016/j.ic.2003.10.004.

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12

Dantchev, Stefan, and Barnaby Martin. "The limits of tractability in Resolution-based propositional proof systems." Annals of Pure and Applied Logic 163, no. 6 (June 2012): 656–68. http://dx.doi.org/10.1016/j.apal.2011.11.001.

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13

Zurek, Eduardo, Mayra Zurbaran, Margarita Gamarra, and Pedro Wightman. "An Implementation of Propositional Logic Resolution Applying a Novel Specific Algebra." Polibits 52 (July 31, 2015): 79–84. http://dx.doi.org/10.17562/pb-52-8.

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14

Zenteno, Flaviano. "Method of resolution of problems and academic performance in propositional logic." SCIÉNDO 21, no. 3 (September 28, 2018): 291–99. http://dx.doi.org/10.17268/sciendo.2018.031.

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15

Arai, Noriko H. "Relative efficiency of propositional proof systems: resolution vs. cut-free LK." Annals of Pure and Applied Logic 104, no. 1-3 (July 2000): 3–16. http://dx.doi.org/10.1016/s0168-0072(00)00005-1.

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16

Xu, Yang, Da Ruan, Etienne E. Kerre, and Jun Liu. "α-Resolution principle based on lattice-valued propositional logic LP(X)." Information Sciences 130, no. 1-4 (December 2000): 195–223. http://dx.doi.org/10.1016/s0020-0255(00)00069-4.

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Ma, Jun, Wenjiang Li, Da Ruan, and Yang Xu. "Filter-based resolution principle for lattice-valued propositional logic LP(X)." Information Sciences 177, no. 4 (February 2007): 1046–62. http://dx.doi.org/10.1016/j.ins.2006.07.027.

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18

Alekhnovich, Michael, Sam Buss, Shlomo Moran, and Toniann Pitassi. "Minimum propositional proof length is NP-hard to linearly approximate." Journal of Symbolic Logic 66, no. 1 (March 2001): 171–91. http://dx.doi.org/10.2307/2694916.

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AbstractWe prove that the problem of determining the minimum propositional proof length is NP-hard to approximate within a factor of . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution. Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs.

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19

Stachniak, Zbigniew, and Peter O’Hearn. "Resolution in the Domain of Strongly Finite Logics." Fundamenta Informaticae 13, no. 3 (July 1, 1990): 333–51. http://dx.doi.org/10.3233/fi-1990-13307.

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In this paper the notion of a resolution counterpart of a propositional logic is introduced and studied. This notion is based on a generalization of the resolution rule of J.A. Robinson. It is shown that for every strongly finite logic a refutationally complete nonclausal resolution proof system can be constructed and that the completeness of such systems is preserved with respect to the polarity and set of support strategies.

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20

Zulaica Hernández, Iker. "Resolving abstract anaphors in Spanish discourse: Underspecification and mereological structures." Linguistics 56, no. 3 (June 26, 2018): 681–713. http://dx.doi.org/10.1515/ling-2018-0008.

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Abstract Anaphoric underspecification involves multiple potential candidate antecedents for an anaphoric expression. In abstract object anaphora, where linguistic antecedents are clauses, sentences and larger fragments of discourse, the source of referential underspecification is commonly found at the propositional level. Thus, underspecified abstract anaphors have multiple antecedents of a higher-order nature (i.e., propositions and events). Following previous research on anaphoric underspecification with nominal antecedents, I propose a hypothetical three-step process toward the resolution of underspecified abstract object anaphors by hearers in discourse: (i) creation of a complex abstract object with a mereological structure that includes all potential interpretations for an anaphor, (ii) recognition of the thematic connection among propositions intended by the speaker in the form of a specific rhetorical relation, and 3) resolution of the abstract anaphor. Potential antecedents for any underspecified abstract anaphor may include atomic propositions and complex abstract referents that result from a merged interpretation of several propositions that are thematically connected. Provided that it is available, I claim that such a merged interpretation, which is part of the mereological structure, is the preferred interpretation as it is generally interpreted as part of a general purpose by the speaker, in addition to contributing to the thematic coherence of discourse.

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21

Kiesl, Benjamin, Adrián Rebola-Pardo, Marijn J. H. Heule, and Armin Biere. "Simulating Strong Practical Proof Systems with Extended Resolution." Journal of Automated Reasoning 64, no. 7 (July 31, 2020): 1247–67. http://dx.doi.org/10.1007/s10817-020-09554-z.

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Abstract Proof systems for propositional logic provide the basis for decision procedures that determine the satisfiability status of logical formulas. While the well-known proof system of extended resolution—introduced by Tseitin in the sixties—allows for the compact representation of proofs, modern SAT solvers (i.e., tools for deciding propositional logic) are based on different proof systems that capture practical solving techniques in an elegant way. The most popular of these proof systems is likely DRAT, which is considered the de-facto standard in SAT solving. Moreover, just recently, the proof system DPR has been proposed as a generalization of DRAT that allows for short proofs without the need of new variables. Since every extended-resolution proof can be regarded as a DRAT proof and since every DRAT proof is also a DPR proof, it was clear that both DRAT and DPR generalize extended resolution. In this paper, we show that—from the viewpoint of proof complexity—these two systems are no stronger than extended resolution. We do so by showing that (1) extended resolution polynomially simulates DRAT and (2) DRAT polynomially simulates DPR. We implemented our simulations as proof-transformation tools and evaluated them to observe their behavior in practice. Finally, as a side note, we show how Kullmann’s proof system based on blocked clauses (another generalization of extended resolution) is related to the other systems.

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22

LIMA, PRISCILA M. V., M. MARIELA M. MORVELI-ESPINOZA, GLAUCIA C. PEREIRA, TALITA O. FERREIRA, and FELIPE M. G. FRANÇA. "LOGICAL REASONING VIA SATISFIABILITY MAPPED INTO ENERGY FUNCTIONS." International Journal of Pattern Recognition and Artificial Intelligence 22, no. 05 (August 2008): 1031–43. http://dx.doi.org/10.1142/s0218001408006673.

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This paper presents the implementation of ARQ-PROP II, a limited-depth propositional neural reasoner based on the Resolution Principle. The SATyrus platform was used in the synthesis of Energy functions from a set of pseudo-Boolean constraints specifying ARQ-PROP II architectures for different inferencing depths. Global minima of the Energy functions produced by SATyrus are associated to SATisfiability of a formula and, in the case of ARQ-PROP II, are associated to Resolution-based refutations. This allows for simplified abduction, prediction and planning to be unified with deduction in a goal-driven style, i.e. there is no need for presetting a reasoning style upon a target set of clauses. Experimental results on deduction with ARQ-PROP II using different propositional depth settings are presented together with a correction of Gadi Pinkas' mapping of SATisfiability into Energy minima.

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23

Liu, Yi, Hairui Jia, and Yang Xu. "Determination of 3-Aryα-Resolution in Lattice-valued Propositional Logic LP(X)." International Journal of Computational Intelligence Systems 6, no. 5 (September 2013): 943–53. http://dx.doi.org/10.1080/18756891.2013.808802.

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24

Constable, Robert, and Wojciech Moczydłowski. "Extracting the resolution algorithm from a completeness proof for the propositional calculus." Annals of Pure and Applied Logic 161, no. 3 (December 2009): 337–48. http://dx.doi.org/10.1016/j.apal.2009.07.008.

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25

Buresh-Oppenheim, Joshua, and Toniann Pitassi. "The complexity of resolution refinements." Journal of Symbolic Logic 72, no. 4 (December 2007): 1336–52. http://dx.doi.org/10.2178/jsl/1203350790.

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AbstractResolution is the most widely studied approach to propositional theorem proving. In developing efficient resolution-based algorithms, dozens of variants and refinements of resolution have been studied from both the empirical and analytic sides. The most prominent of these refinements are: DP (ordered), DLL (tree), semantic, negative, linear and regular resolution. In this paper, we characterize and study these six refinements of resolution. We give a nearly complete characterization of the relative complexities of all six refinements. While many of the important separations and simulations were already known, many new ones are presented in this paper; in particular, we give the first separation of semantic resolution from general resolution. As a special case, we obtain the first exponential separation of negative resolution from general resolution. We also attempt to present a unifying framework for studying all of these refinements.

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26

Giunchiglia, E., M. Narizzano, and A. Tacchella. "Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas." Journal of Artificial Intelligence Research 26 (August 17, 2006): 371–416. http://dx.doi.org/10.1613/jair.1959.

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Resolution is the rule of inference at the basis of most procedures for automated reasoning. In these procedures, the input formula is first translated into an equisatisfiable formula in conjunctive normal form (CNF) and then represented as a set of clauses. Deduction starts by inferring new clauses by resolution, and goes on until the empty clause is generated or satisfiability of the set of clauses is proven, e.g., because no new clauses can be generated. In this paper, we restrict our attention to the problem of evaluating Quantified Boolean Formulas (QBFs). In this setting, the above outlined deduction process is known to be sound and complete if given a formula in CNF and if a form of resolution, called ``Q-resolution'', is used. We introduce Q-resolution on terms, to be used for formulas in disjunctive normal form. We show that the computation performed by most of the available procedures for QBFs --based on the Davis-Logemann-Loveland procedure (DLL) for propositional satisfiability-- corresponds to a tree in which Q-resolution on terms and clauses alternate. This poses the theoretical bases for the introduction of learning, corresponding to recording Q-resolution formulas associated with the nodes of the tree. We discuss the problems related to the introduction of learning in DLL based procedures, and present solutions extending state-of-the-art proposals coming from the literature on propositional satisfiability. Finally, we show that our DLL based solver extended with learning, performs significantly better on benchmarks used in the 2003 QBF solvers comparative evaluation.

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27

He, X., J. Liu, Y. Xu, L. Martinez, and D. Ruan. "On -satisfiability and its -lock resolution in a finite lattice-valued propositional logic." Logic Journal of IGPL 20, no. 3 (February 11, 2011): 579–88. http://dx.doi.org/10.1093/jigpal/jzr007.

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28

Wallis, Steven E., and Bernadette Wright. "Integrative propositional analysis for understanding and reducing poverty." Kybernetes 48, no. 6 (June 3, 2019): 1264–77. http://dx.doi.org/10.1108/k-03-2018-0136.

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Purpose Current approaches to understanding and resolving the problem of poverty have not proved effective. This paper aims to provide a new explanation of why we have failed and what must be done to improve our understanding, decision-making, action and success. Design/methodology/approach Integrative propositional analysis is used to evaluate and synthesize theoretical and practical perspectives on poverty from five academic disciplines and five disparate organizations. Findings Individual theoretical perspectives were found to have low levels of complexity and systemicity. Research limitations/implications Clear research directions are shown to accelerate improvements in understanding. Additionally, results may provide a useful guide for developing computer models of poverty. Practical implications The causal knowledge map of synthesized theories suggests where practice may be relatively effective and where unanticipated consequences are more likely to occur. Social implications Policy decision-making to address the problem of poverty is not likely to lead to successful resolution. Thus, poverty is likely to continue until we develop a more systemic understanding. Originality/value This interdisciplinary paper provides a new structural perspective on why we have not been able to solve the poverty problem – and shows how far we have yet to go to reach success.

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29

Alonderis, Romas, and Haroldas Giedra. "A derivation-loop method for temporal logic." Lietuvos matematikos rinkinys 60 (November 12, 2019): 1–6. http://dx.doi.org/10.15388/lmr.a.2019.14953.

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Various types of calculi (Hilbert, Gentzen sequent, resolution calculi, tableaux) for propositional linear temporal logic (PLTL) have been considered in the literature. Cutfree Gentzen-type sequent calculi are convenient tools for backward proof-search search of formulas and sequents. In this paper we present a cut-free Gentzen type sequent calculus for PLTL with the operator

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30

CIABATTONI, AGATA, and ALEXANDER LEITSCH. "Towards an algorithmic construction of cut-elimination procedures." Mathematical Structures in Computer Science 18, no. 1 (February 2008): 81–105. http://dx.doi.org/10.1017/s0960129507006573.

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We investigate cut elimination in propositional substructural logics. The problem is to decide whether a given calculus admits (reductive) cut elimination. We show that for commutative single-conclusion sequent calculi containing generalised knotted structural rules and arbitrary logical rules the problem can be decided by resolution-based methods. A general cut-elimination proof for these calculi is also provided.

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31

Schroeder-Heister, Peter. "Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen." Bulletin of Symbolic Logic 8, no. 2 (June 2002): 246–65. http://dx.doi.org/10.2178/bsl/1182353872.

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AbstractIn the 1920s, Paul Hertz (1881–1940) developed certain calculi based on structural rules only and established normal form results for proofs. It is shown that he anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory. Furthermore, it is shown that Gentzen, in his first paper of 1933, which heavily draws on Hertz, proves a normal form result which corresponds to the completeness of propositional SLD-resolution in logic programming.

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Lempp, Frieder. "A software implementation and case study application of Lempp’s propositional model of conflict resolution." International Journal of Conflict Management 28, no. 5 (October 9, 2017): 563–91. http://dx.doi.org/10.1108/ijcma-08-2016-0073.

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Purpose The starting point of this paper is the propositional model of conflict resolution which was presented and critically discussed in Lempp (2016). Based on this model, a software implementation, called ProCON, is introduced and applied to three scenarios. The purpose of the paper is to demonstrate how ProCON can be used by negotiators and to evaluate ProCON’s practical usefulness as an automated negotiation support system. Design/methodology/approach The propositional model is implemented as a computer program. The implementation consists of an input module to enter data about a negotiation situation, an output module to generate outputs (e.g. a list of all incompatible goal pairs or a graph displaying the compatibility relations between goals) and a queries module to run queries on particular aspects of a negotiation situation. Findings The author demonstrates how ProCON can be used to capture a simple two-party, non-iterative prisoner’s dilemma, applies ProCON to a contract negotiation between a supplier and a purchaser of goods, and uses it to model the negotiations between the Iranian and six Western governments over Iran’s nuclear enrichment and stockpiling capacities. Research limitations/implications A limitation of the current version of ProCON arises from the fact that the computational complexity of the underlying algorithm is EXPTIME (i.e. the computing time required to process information in ProCON grows exponentially with respect to the number of issues fed into the program). This means that computing time can be quite long for even relatively small negotiation scenarios. Practical implications The three case studies demonstrate how ProCON can provide support for negotiators in a wide range of multi-party, multi-issue negotiations. In particular, ProCON can be used to visualise the compatibility relations between parties’ goals, generate possible outcomes and solutions and evaluate solutions regarding the extent to which they satisfy the parties’ goals. Originality/value In contrast to standard game-theoretic models of negotiation, ProCON does not require users to provide data about their preferences across their goals. Consequently, it can operate in situations where no information about the parties’ goal preferences is available. Compared to game-theoretical models, ProCON represents a more general approach of looking at possible outcomes in the context of negotiations.

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HARALICK, ROBERT M., and SHEAU-HUEI WU. "AN APPROXIMATE LINEAR TIME PROPAGATE AND DIVIDE THEOREM PROVER FOR PROPOSITIONAL LOGIC." International Journal of Pattern Recognition and Artificial Intelligence 01, no. 01 (April 1987): 141–55. http://dx.doi.org/10.1142/s0218001487000102.

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For theorem proving in the propositional calculus, we describe a semantic non-resolution based propagate and divide algorithm using the three principles of: reducing a potential theorem size by appropriate substitutions and simplifications; minimizing tree branching by using matching to carry out complete constraint propagation; and choosing alternatives which efficiently solve the subproblem currently being worked on. We provide experimental evidence based on almost 240,000 experiments indicating that this propagate and divide algorithm needs, on the average, approximately a linear amount of computation time as a function of problem size (length of well-formed formula) to prove a theorem in the propositional calculus. Furthermore, the computation time seems to depend only on the length of the well-formed formula and not on the number of distinct atoms in the well-formed formula.

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KumarDey, Dipanjan. "How Does Resolution Works in Propositional Calculus and Predicate Calculus, Introduction to Unification and Substitution." International Journal of Computer Applications 99, no. 10 (August 20, 2014): 22–31. http://dx.doi.org/10.5120/17409-7983.

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35

Xu, Weitao, Wenqiang Zhang, Dexian Zhang, Yang Xu, and Xiaodong Pan. "α-Resolution Method for Lattice-valued Horn Generalized Clauses in Lattice-valued Propositional Logic Systems." International Journal of Computational Intelligence Systems 8, sup1 (December 11, 2015): 75–84. http://dx.doi.org/10.1080/18756891.2015.1129580.

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Yamasaki, Susumu, and Shuji Doshita. "Resolution deduction to detect satisfiability for another class including non-horn sentences in propositional logic." Information Processing Letters 23, no. 4 (November 1986): 201–7. http://dx.doi.org/10.1016/0020-0190(86)90136-5.

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37

Zhang, Jiafeng, Yang Xu, and Xingxing He. "α-Generalized Semantic Resolution Method in Linguistic Truth-valued Propositional LogicLV(n×2)P(X)." International Journal of Computational Intelligence Systems 7, no. 1 (October 23, 2013): 160–71. http://dx.doi.org/10.1080/18756891.2013.857895.

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38

WALICKI, MICHAŁ. "RESOLVING INFINITARY PARADOXES." Journal of Symbolic Logic 82, no. 2 (June 2017): 709–23. http://dx.doi.org/10.1017/jsl.2016.18.

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AbstractGraph normal form, GNF, [1], was used in [2, 3] for analyzing paradoxes in propositional discourses, with the semantics—equivalent to the classical one—defined by kernels of digraphs. The paper presents infinitary, resolution-based reasoning with GNF theories, which is refutationally complete for the classical semantics. Used for direct (not refutational) deduction it is not explosive and allows to identify in an inconsistent discourse, a maximal consistent subdiscourse with its classical consequences. Semikernels, generalizing kernels, provide the semantic interpretation.

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Zhou, Jun Ping, Chun Guang Zhou, Ming Hao Yin, and Hui Yang. "Extension Rule Based Model Counting Using More Reasoning." Advanced Materials Research 108-111 (May 2010): 268–73. http://dx.doi.org/10.4028/www.scientific.net/amr.108-111.268.

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Extension rule is a new method for computing the number of models for a given propositional formula. In some sense, it is actually an inverse propositonal resolution. In order to improve counting performance, we introduce some reasoning rules into extension rule based model counting and present a new algorithm RCER which combines the extension rule and the reasoning rule together. The experiment results show that the algorithm not only occupies less space but also increases the efficiency for solving model counting.

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Nath Maurya, Vishwa, and Avadhesh Kumar Maurya. "Polynomial Simulation and Refutation of Complex Formulas of Resolution over Linear Equations in Propositional Proof System." American Journal of Modeling and Optimization 2, no. 1 (March 16, 2014): 34–38. http://dx.doi.org/10.12691/ajmo-2-1-5.

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41

Dieu, Phan Dinh, and Phan Hong Giang. "Interval –valued probabilistic logic for logic programs." Journal of Computer Science and Cybernetics 10, no. 3 (April 15, 2016): 1–13. http://dx.doi.org/10.15625/1813-9663/10/3/8193.

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This paper presents an approximate method for probabilistic entailment problem in knowledge bases where a portion of knowledge is given by a sentence in propositional logic accompanied with an interval presenting its truth probalibity. This method reduces the entailment problem to one of finding “prime implicants” of the target sentence expressed through sentences in the given knowledge base. It is shown that in the case of probabilistic logic programs the set of such prime implicants can be found by using the SLD-resolution method for usual definte logic programs.

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42

Lempp, Frieder. "A logic-based model for resolving conflicts." International Journal of Conflict Management 27, no. 1 (February 8, 2016): 116–39. http://dx.doi.org/10.1108/ijcma-11-2014-0081.

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Purpose – The purpose of this paper is to explore the extent to which formal logic can be applied to conflict analysis and resolution. It is motivated by the idea that conflicts can be understood as inconsistent sets of interests. Design/methodology/approach – A simple propositional model, based on propositional logic, which can be used to analyze conflicts, has been introduced and four algorithms have been presented to generate possible solutions to a conflict. The model is illustrated by applying it to the conflict between the Obama administration and the Syrian Government in September 2013 over the destruction of Syria’s chemical weapons programme. Findings – The author shows how different solutions, such as compromises, minimally invasive solutions or solutions compatible with certain pre-defined norms, can be generated by the model. It is shown how the model can operate in situations where the game-theoretic model fails due to a lack of information about the parties’ utility values. Research limitations/implications – The model can be used as a theoretical framework for future experimental research and/or to trace the course of particular conflict scenarios. Practical implications – The model can be used as the basis for building software applications for conflict resolution practitioners, such as negotiators or mediators. Originality/value – While the idea of using logic to analyse the structure of conflicts and generate possible solutions is not new to the field of conflict studies, the model presented in this paper provides a novel way of understanding conflicts for both researchers and practitioners.

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43

Gaysin, Azza. "ℋ-Colouring Dichotomy in Proof Complexity." Journal of Logic and Computation 31, no. 5 (April 24, 2021): 1206–25. http://dx.doi.org/10.1093/logcom/exab028.

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Abstract The $\mathcal {H}$-colouring problem for undirected simple graphs is a computational problem from a huge class of the constraint satisfaction problems (CSPs): an $\mathcal {H}$-colouring of a graph $\mathcal {G}$ is just a homomorphism from $\mathcal {G}$ to $\mathcal {H}$ and the problem is to decide for fixed $\mathcal {H}$, given $\mathcal {G}$, if a homomorphism exists or not. The dichotomy theorem for the $\mathcal {H}$-colouring problem was proved by Hell and Nešetřil (1990, J. Comb. Theory Ser. B, 48, 92–110) (an analogous theorem for all CSPs was recently proved by Zhuk (2020, J. ACM, 67, 1–78) and Bulatov (2017, FOCS, 58, 319–330)), and it says that for each $\mathcal {H}$, the problem is either $p$-time decidable or $NP$-complete. Since negations of unsatisfiable instances of CSP can be expressed as propositional tautologies, it seems to be natural to investigate the proof complexity of CSP. We show that the decision algorithm in the $p$-time case of the $\mathcal {H}$-colouring problem can be formalized in a relatively weak theory and that the tautologies expressing the negative instances for such $\mathcal {H}$ have polynomial proofs in propositional proof system $R^*(log)$, a mild extension of resolution. In fact, when the formulas are expressed as unsatisfiable sets of clauses, they have $p$-size resolution proofs. To establish this, we use a well-known connection between theories of bounded arithmetic and propositional proof systems. This upper bound follows also from a different construction in [1]. We complement this result by a lower bound result that holds for many weak proof systems for a special example of $NP$-complete case of the $\mathcal {H}$-colouring problem, using known results about the proof complexity of the pigeonhole principle. The main goal of our work is to start the development of some of the theories beyond the CSP dichotomy theorem in bounded arithmetic. We aim eventually—in a subsequent work—to formalize in such a theory the soundness of Zhuk’s algorithm, extending the upper bound proved here from undirected simple graphs to the general case of directed graphs in some logical calculi.

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Bimpikou, Sofia, Emar Maier, and Petra Hendriks. "The discourse structure of free indirect discourse reports." Linguistics in the Netherlands 38 (October 29, 2021): 21–39. http://dx.doi.org/10.1075/avt.00048.bim.

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Abstract We investigate the discourse structure of Free Indirect Discourse passages in narratives. We argue that Free Indirect Discourse reports consist of two separate propositional discourse units: an (explicit or implicit) frame segment and a reported content. These segments are connected at the level of discourse structure by a non-veridical, subordinating discourse relation of Attribution, familiar from recent SDRT analyses of indirect discourse constructions in natural conversation (Hunter, 2016). We conducted an experiment to detect the covert presence of a subordinating frame segment based on its effects on pronoun resolution. We compared (unframed) Free Indirect Discourse with overtly framed Indirect Discourse and a non-reportative segment. We found that the first two indeed pattern alike in terms of pronoun resolution, which we take as evidence against the pragmatic context split approach of Schlenker (2004) and Eckardt (2014), and in favor of our discourse structural Attribution analysis.

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45

Fretheim, Thorstein, Nana Aba Appiah Amfo, and Ildikó Vaskó. "Token-reflexive, anaphoric and deictic functions of ‘here’." Nordic Journal of Linguistics 34, no. 3 (December 2011): 239–94. http://dx.doi.org/10.1017/s0332586512000030.

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There are basically three ways in which the reference of a token of the English proximal spatial indexicalhereand corresponding terms in other languages can be resolved in the context-dependent, pragmatic phase of the addressee's determination of the propositional content of an utterance that contains this adverbial adjunct. ‘Here’ may refer reflexively to the place of utterance, including minimally the spot occupied by the speaker (token-reflexive reference), it may be anaphoric upon a discourse antecedent that provides information necessary for identification of the referent (anaphoric reference), or resolution of the reference depends on information derived from processing of a perceptual stimulus (deictic reference). These three pragmatic paths to resolution of the reference of proximal spatial indexicals are not mutually exclusive, so they do not warrant postulation of lexical ambiguity, at least not the traditional kind of ambiguity based on differences in conceptual meaning.

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46

CHATALIC, PHILIPPE, and LAURENT SIMON. "MULTIRESOLUTION FOR SAT CHECKING." International Journal on Artificial Intelligence Tools 10, no. 04 (December 2001): 451–81. http://dx.doi.org/10.1142/s0218213001000611.

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This paper presents a system based on new operators for handling sets of propositional clauses compactly represented by means of ZBDDs. The high compression power of such data structures allows efficient encodings of structured instances. A specialized operator for the distribution of sets of clauses is introduced and used for performing multiresolution on clause sets. Cut eliminations between sets of clauses of exponential size may then be performed using polynomial size data structures. The ZRES system, a new implementation of the Davis-Putnam procedure of 1960, solves two hard problems for resolution, that are currently out of the scope of the best SAT provers.

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47

Jayme, Fernando Gonzaga, and Victor Barbosa Dutra. "Dejudicialization and Proceduralism Based on the Nature of Conflicts and According to the Brazilian Constitution." REVISTA INTERNACIONAL CONSINTER DE DIREITO 13, no. 13 (December 21, 2021): 341–56. http://dx.doi.org/10.19135/revista.consinter.00013.16.

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The objective of this paper is to show that Access to Justice is a broader concept than Access to the Judiciary. Apart from the movements for access to justice, it is the intention to prove that the Alternative Means of Dispute Resolution and the studies of Conflict Perspective are equally relevant, having in mind that they both defend a plurality of conflict processing institutions (state or not), based on the hypothesis that dejudicialization is an important way to strengthen institutions and promote economic and social development. Therefore, the deductive approach method was used in conjunction with the propositional-juridical method to demonstrate that the exhaustion of the state-owned model in solving conflicts shows that it is possible (and necessary) to develop the Proceduralism beyond the scope of the Judiciary, in order to institutionally expand forms of conflict resolution in civil society. From this, the concept of Proceduralism arises, interconnected with the due process and which is also suitable for the out-of-court ways of dispute resolution, in order to achieve adequate, effective and due process protection, so that pacification is carried out along the lines of constitutional guarantees, with constitutional procedurality also acting on the unjudicialized means of resolving conflicts.

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48

BUSS, SAMUEL R., LESZEK ALEKSANDER KOŁODZIEJCZYK, and NEIL THAPEN. "FRAGMENTS OF APPROXIMATE COUNTING." Journal of Symbolic Logic 79, no. 2 (June 2014): 496–525. http://dx.doi.org/10.1017/jsl.2013.37.

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AbstractWe study the long-standing open problem of giving $\forall {\rm{\Sigma }}_1^b$ separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the $\forall {\rm{\Sigma }}_1^b$ Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FPNP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of $T_2^1$ augmented with the surjective weak pigeonhole principle for polynomial time functions.

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49

Krajíček, Jan. "Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic." Journal of Symbolic Logic 62, no. 2 (June 1997): 457–86. http://dx.doi.org/10.2307/2275541.

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AbstractA proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: (1)Feasible interpolation theorems for the following proof systems:(a)resolution(b)a subsystem of LK corresponding to the bounded arithmetic theory (α)(c)linear equational calculus(d)cutting planes.(2)New proofs of the exponential lower bounds (for new formulas)(a)for resolution ([15])(b)for the cutting planes proof system with coefficients written in unary ([4]).(3)An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds in the bounded arithmetic theory (α).In the other direction we show that a depth 2 subsystem of LK does not admit feasible monotone interpolation theorem (the so called Lyndon theorem), and that a feasible monotone interpolation theorem for the depth 1 subsystem of LK would yield new exponential lower bounds for resolution proofs of the weak pigeonhole principle.

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50

Nkouankou, Aboubakar, Fotso Clarice, Wadoufey Abel, and René Ndoundam. "Pre-image attack of the MD5 hash function by proportional logic." International Journal of Research and Innovation in Applied Science 07, no. 08 (2022): 20–25. http://dx.doi.org/10.51584/ijrias.2022.7802.

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Hash functions are important cryptographic primitives that map arbitrary length messages to fixed length message summaries such that: it is easy to compute the digest given a message, while invert the hash process (for example, finding a message that maps a summary of a specific message) is difficult. An attack against a hash function is an algorithm that nevertheless manages to invert the hash process. Hash functions are used in authentication, digital signature, and key exchange systems. The most widely used hash function in many applications is the Message Digest-5 (MD5) algorithm. In this paper we study the current state of the technique of realization of the preimage attack of MD5 using solver SAT, we try improvements in the process of encoding and resolution. An important part of our work is to use the methods of propositional logic to model the attack problem and to determine which heuristic leads to the best resolution. Our most important result is a new encoding of the addition to several operands which considerably reduce the time required for the SAT solvers to find a solution to coding’s previously known.

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