Logic Programming and Automated Reasoning最新文献

{"title":"Formally Proving the Boolean Pythagorean Triples Conjecture","authors":"L. Cruz-Filipe, Peter Schneider-Kamp","doi":"10.29007/jvdj","DOIUrl":"https://doi.org/10.29007/jvdj","url":null,"abstract":"In 2016, Heule, Kullmann and Marek solved the Boolean Pythagorean Triples problem: is there a binary coloring of the natural numbers such that every Pythagorean triple contains an element of each color? By encoding a finite portion of this problem as a propositional formula and showing its unsatisfiability, they established that such a coloring does not exist. Subsequently, this answer was verified by a correct-by-construction checker extracted from a Coq formalization, which was able to reproduce the original proof. However, none of these works address the question of formally addressing the relationship between the propositional formula that was constructed and the mathematical problem being considered. In this work, we formalize the Boolean Pythagorean Triples problem in Coq. We recursively define a family of propositional formulas, parameterized on a natural number n , and show that unsatisfiability of this formula for any particular n implies that there does not exist a solution to the problem. We then formalize the mathematical argument behind the simplification step in the original proof of unsatisfiability and the logical argument underlying cube-and-conquer, obtaining a verified proof of Heule et al. ’s solution.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128016076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Synchronizing Constrained Horn Clauses","authors":"D. Mordvinov, Grigory Fedyukovich","doi":"10.29007/gr5c","DOIUrl":"https://doi.org/10.29007/gr5c","url":null,"abstract":"Simultaneous occurrences of multiple recurrence relations in a system of non-linear constrained Horn clauses are crucial for proving its satisfiability. A solution of such system is often inexpressible in the constraint language. We propose to synchronize recurrent computations, thus increasing the chances for a solution to be found. We introduce a notion of CHC product allowing to formulate a lightweight iterative algorithm of merging recurrent computations into groups and prove its soundness. The evaluation over a set of systems handling lists and linear integer arithmetic confirms that the transformed systems are drastically more simple to solve than the original ones.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133478606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A One-Pass Tree-Shaped Tableau for LTL+Past","authors":"N. Gigante, A. Montanari, Mark Reynolds","doi":"10.29007/3hb9","DOIUrl":"https://doi.org/10.29007/3hb9","url":null,"abstract":"Linear Temporal Logic (LTL) is a de-facto standard formalism for expressing properties of systems and temporal constraints in formal verification, artificial intelligence, and other areas of computer science. The problem of LTL satisfiability is thus prominently important to check the consistency of these temporal specifications. Although adding past operators to LTL does not increase its expressive power, recently the interest for explicitly handling the past in temporal logics has increased because of the clarity and succinctness that those operators provide. In this work, a recently proposed one-pass tree-shaped tableau system for LTL is extended to support past operators. The modularity of the required changes provides evidence for the claimed ease of extensibility of this tableau system.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123869274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Seminator: A Tool for Semi-Determinization of Omega-Automata","authors":"František Blahoudek, A. Duret-Lutz, Mikulás Klokocka, M. Kretínský, J. Strejček","doi":"10.29007/k5nl","DOIUrl":"https://doi.org/10.29007/k5nl","url":null,"abstract":"We present a tool that transforms nondeterministic omega-automata to semi-deterministic omega-automata. The tool Seminator accepts transition-based generalized Buchi automata (TGBA) as an input and produces automata with two kinds of semi-determinism. The implemented procedure performs degeneralization and semi-determinization simultaneously and employs several other optimizations. We experimentally evaluate Seminator in the context of LTL to semi-deterministic automata translation.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131504831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"First-Order Interpolation and Interpolating Proof Systems","authors":"L. Kovács, A. Voronkov","doi":"10.29007/1qb8","DOIUrl":"https://doi.org/10.29007/1qb8","url":null,"abstract":"It is known that one can extract Craig interpolants from so-called local derivations. An interpolant extracted from such a derivation is a boolean combination of formulas occurring in the derivation. However, standard complete proof systems, such as superposition, for theories having the interpolation property are not necessarily complete for local proofs. In this paper we investigate interpolant extraction from non-local refutations (proofs of contradiction) in the superposition calculus and prove a number of general results about interpolant extraction and complexity of extracted interpolants. In particular, we prove that the number of quantifier alternations in first-order interpolants of formulas without quantifier alternations is unbounded. The proof of this result relies on a small number of assumptions about the theory and the proof system, so it also applies to many first-order theories beyond predicate logic. This result has far-reaching consequences for using local proofs as a foundation for interpolating proof systems any such proof system should deal with formulas of arbitrary quantifier complexity. To search for alternatives for interpolating proof systems, we consider several variations on interpolation and local proofs. Namely, we give an algorithm for building interpolants from resolution refutations in logic without equality and discuss additional constraints when this approach can be also used for logic with equality. We finally propose a new direction related to interpolation via local proofs in first-order theories.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128570278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Formalization of some central theorems in combinatorics of finite sets","authors":"Abhishek Kr Singh","doi":"10.29007/r7fg","DOIUrl":"https://doi.org/10.29007/r7fg","url":null,"abstract":"We present fully formalized proofs of some central theorems from combinatorics. These are Dilworth's decomposition theorem, Mirsky's theorem, Hall's marriage theorem and the ErdH{o}s-Szekeres theorem. Dilworth's decomposition theorem is the key result among these. It states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mirsky's theorem is a dual of Dilworth's decomposition theorem, which states that in any finite poset, the size of a smallest antichain cover and a largest chain are the same. We use Dilworth's theorem in the proofs of Hall's Marriage theorem and the ErdH{o}s-Szekeres theorem. The combinatorial objects involved in these theorems are sets and sequences. All the proofs are formalized in the Coq proof assistant. We develop a library of definitions and facts that can be used as a framework for formalizing other theorems on finite posets.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"252 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131807726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep Network Guided Proof Search","authors":"Sarah M. Loos, G. Irving, Christian Szegedy, C. Kaliszyk","doi":"10.29007/8MWC","DOIUrl":"https://doi.org/10.29007/8MWC","url":null,"abstract":"Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification.Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved.Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116091292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Conflicts and Strategies in QBF","authors":"N. Bjørner, Mikoláš Janota, William Klieber","doi":"10.29007/4sk1","DOIUrl":"https://doi.org/10.29007/4sk1","url":null,"abstract":"QBF solving techniques can be divided into the DPLL-based and expansion-based. In this paper we look at how these two techniques can be combined while using strategy extraction as a means of interaction between the two. Once propagation derives a conflict for one of the players, we analyse the proof of such and devise a strategy for the opponent. Subsequently, this strategy is used to constrain the losing player. The implemented prototype shows feasibility of the approach. A number of avenues for future research can be envisioned. Can strategies be employed in a different fashion? Can better strategy be constructed? Do the presented techniques generalize beyond QBF?","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"172 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116289145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Lightweight Double-negation Translation","authors":"Frédéric Gilbert","doi":"10.29007/vbs5","DOIUrl":"https://doi.org/10.29007/vbs5","url":null,"abstract":"Deciding whether a classical theorem can be proved constructively is a well-known undecidable problem. As a consequence, any computable double-negation translation inserts some unnecessary double negations. This paper shows that most of these unnecessary insertions can be avoided without any use of constructive proof search techniques. For this purpose, we restrict the analysis to syntax-directed double-negation translations, which translate a proposition through a single traversal – and include most of the usual translations such as Kolmogorov's, Godel-Gentzen's, and Kuroda's. A partial order among translations are presented to select translations avoiding as many double negations as possible. This order admits a unique minimal syntax-directed translation with noticeable properties.","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114069760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Automated Theorem Proving by Translation to Description Logic","authors":"Negin Arhami, G. Sutcliffe","doi":"10.29007/xgq9","DOIUrl":"https://doi.org/10.29007/xgq9","url":null,"abstract":"of a dissertation at the University of Miami. Thesis supervised by Professor Geoff Suttcliffe. No. of pages in text. (132) Many Automated Theorem Proving (ATP) systems for different logical forms, and translators for translating different logical forms from one to another, have been developed and are now available. Some logical forms are more expressive than others, and it is easier to express problems in those logical forms. On the other hand, the ATP systems for less expressive forms have benefited from more years of development and testing. There is a trade-off between the expressivity of a logical form, and the capabilities of the available ATP systems. Different ATP systems and translators can be combined to solve a problem expressed in a given logical form. In this research, an experiment has been designed and carried out to compare all different possible ways of trying to solve a problem, using the following logical forms in increasing order of expressivity: Propositional Logic, Description Logic, Effectively Propositional form, Conjunctive Normal Form, First Order Form, Typed First order form-monomorphic, Typed First order form-polymorphic, Typed Higher order form-monomorphic. In this dissertation, the properties, syntax, and semantics of each target logical form are briefly described. For each form, the most popular ATP systems and translators for translating to less expressive forms are introduced. Problems in logics more expressive than Conjunctive Normal Form can be translated directly to Conjunctive Normal Form, or indirectly by translation via intermediate logics. No translator was available to translate from Conjunctive Normal Form to Description Logic, which sits between Effectively Propositional form and Propositional Logic in terms of expressivity. Saffron a Conjunctive Normal Form to Description Logic translator, has been developed, which fills the gap between Conjunctive Normal Form and Description Logic. Moreover, Description Logic Form (DLF), a new syntax for Description Logic, has been designed. Automated theorem proving by translation to Description Logic is now an alternative way of solving problems expressed in logics more expressive than Description Logic, by combining necessary translators from those logics to Conjunctive Normal Form, Saffron, and a Description Logic ATP system. For My Family, My Strength, My Backbone, and My Role Models: Ahmad Arhami, Masomeh Parchamdar, Dr. Ashkon Arhami, Dr. Ehsan Arhami, and Moeindokht Arhami","PeriodicalId":207621,"journal":{"name":"Logic Programming and Automated Reasoning","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114193904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}