Relevant bibliographies by topics / Propositional logic

Academic literature on the topic 'Propositional logic'

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Published: 4 June 2021

Last updated: 22 June 2024

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Journal articles on the topic "Propositional logic"

WHITEN, BILL. "A SIMPLE ALGORITHM FOR DEDUCTION." ANZIAM Journal 51, no. 1 (July 2009): 102–22. http://dx.doi.org/10.1017/s1446181109000352.

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AbstractIt is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.

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Al-Khowarizmi, Al-Khowarizmi, Asrar Aspia Manurung, and Mulkan Azhari. "Design of an Application to Calculate Student Grades in Learning Logic Informatics Propositional Calculus Material." Hanif Journal of Information Systems 1, no. 1 (August 24, 2023): 18–25. http://dx.doi.org/10.56211/hanif.v1i1.7.

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Propositional calculus is a method used to calculate the truth value of a proposition. Propositional calculus is commonly studied by various students, from high school to college. Propositional calculus studies the truth value (True/False) of a proposition. The proposition is then processed into the steps of working on the proposition according to the order of operator priority, which is packaged into truth tables and logical expressions. The proposition work done is not easy, but consumes a lot of time and writing media if done manually. Errors in doing proposition work result in inaccurate truth values obtained. Therefore, the author is interested in making an application to calculate student grades using the propositional calculus method that can be used to overcome the problem of working on propositions manually, so that it can produce accurate truth values, which can also be used as a learning medium and media for students to calculate and see the results of their grades manually.

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Bedregal, Benjamín René Callejas, and Anderson Paiva Cruz. "Propositional Logic as a Propositional Fuzzy Logic." Electronic Notes in Theoretical Computer Science 143 (January 2006): 5–12. http://dx.doi.org/10.1016/j.entcs.2005.05.023.

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Citkin, Alex. "Deductive systems with unified multiple-conclusion rules." Logical Investigations 26, no. 2 (December 13, 2020): 87–105. http://dx.doi.org/10.21146/2074-1472-2020-26-2-87-105.

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Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and are being treated in the same way. The suggested approach is based on the ideas of Ƚukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. A special attention is paid to the logics in which each proposition is either accepted or rejected.

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FRITZ, PETER. "LOGICS FOR PROPOSITIONAL CONTINGENTISM." Review of Symbolic Logic 10, no. 2 (March 20, 2017): 203–36. http://dx.doi.org/10.1017/s1755020317000028.

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AbstractRobert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting logic containing an existential quantifier is not recursively axiomatizable, as it is recursively isomorphic to second-order logic, and a natural candidate axiomatization for the resulting logic containing an existential operator is shown to be incomplete.

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Gehrke, Mai, Carol Walker, and Elbert Walker. "A Mathematical Setting for Fuzzy Logics." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 05, no. 03 (June 1997): 223–38. http://dx.doi.org/10.1142/s021848859700021x.

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The setup of a mathematical propositional logic is given in algebraic terms, describing exactly when two choices of truth value algebras give the same logic. The propositional logic obtained when the algebra of truth values is the real numbers in the unit interval equipped with minimum, maximum and -x=1-x for conjunction, disjunction and negation, respectively, is the standard propositional fuzzy logic. This is shown to be the same as three-valued logic. The propositional logic obtained when the algebra of truth values is the set {(a, b)|a≤ b and a,b∈[0,1]} of subintervals of the unit interval with component-wise operations, is propositional interval-valued fuzzy logic. This is shown to be the same as the logic given by a certain four element lattice of truth values. Since both of these logics are equivalent to ones given by finite algebras, it follows that there are finite algorithms for determining when two statements are logically equivalent within either of these logics. On this topic, normal forms are discussed for both of these logics.

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O'Hearn, Peter W., and David J. Pym. "The Logic of Bunched Implications." Bulletin of Symbolic Logic 5, no. 2 (June 1999): 215–44. http://dx.doi.org/10.2307/421090.

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AbstractWe introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers and which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels.

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Gärdenfors, Peter. "Propositional logic based on the dynamics of belief." Journal of Symbolic Logic 50, no. 2 (June 1985): 390–94. http://dx.doi.org/10.2307/2274226.

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In this article propositions will be identified with a certain kind of changes of belief. The intended interpretation is that a proposition is characterised by the change it would induce if added to a state of belief. Propositions will thus be defined as functions from states of belief to states of belief. A set of postulates concerning the properties and existence of propositions will be formulated. A proposition will be said to be a tautology iff it is the identity function on states of belief. The main result is that the logic determined by the set of postulates is intuitionistic propositional logic.The basic epistemic concept is that of a belief model, which is defined as a pair 〈, 〉, where is a nonempty set and is a class of functions from to . The elements in will be called states of belief and they will be denoted K, K′,…. A discussion of the epistemological interpretation of the states of belief can be found in Gärdenfors [2]. Here, no assumptions about the structure of the elements in will be made.The elements in will be called propositions, and A, B, C, … will be used as variables over . Functions from states of belief to states of belief can be characterised as epistemic inputs. The intended interpretation of the functions in is that they correspond to changes of belief where the new evidence is accepted as “certain” or “known” in the resulting state of belief. This means that not all functions defined on can properly be called propositions.

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MAHER, MICHAEL J. "Propositional defeasible logic has linear complexity." Theory and Practice of Logic Programming 1, no. 6 (November 2001): 691–711. http://dx.doi.org/10.1017/s1471068401001168.

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Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.

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DZIK, WOJCIECH, and PIOTR WOJTYLAK. "UNIFICATION IN SUPERINTUITIONISTIC PREDICATE LOGICS AND ITS APPLICATIONS." Review of Symbolic Logic 12, no. 1 (December 3, 2018): 37–61. http://dx.doi.org/10.1017/s1755020318000011.

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AbstractWe introduce unification in first-order logic. In propositional logic, unification was introduced by S. Ghilardi, see Ghilardi (1997, 1999, 2000). He successfully applied it in solving systematically the problem of admissibility of inference rules in intuitionistic and transitive modal propositional logics. Here we focus on superintuitionistic predicate logics and apply unification to some old and new problems: definability of disjunction and existential quantifier, disjunction and existential quantifier under implication, admissible rules, a basis for the passive rules, (almost) structural completeness, etc. For this aim we apply modified specific notions, introduced in propositional logic by Ghilardi, such as projective formulas, projective unifiers, etc.Unification in predicate logic seems to be harder than in the propositional case. Any definition of the key concept of substitution for predicate variables must take care of individual variables. We allow adding new free individual variables by substitutions (contrary to Pogorzelski & Prucnal (1975)). Moreover, since predicate logic is not as close to algebra as propositional logic, direct application of useful algebraic notions of finitely presented algebras, projective algebras, etc., is not possible.

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Dissertations / Theses on the topic "Propositional logic"

Barbosa, Fábio Daniel Moreira. "Probabilistic propositional logic." Master's thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/22198.

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Mestrado em Matemática e Aplicações
O termo Lógica Probabilística, em geral, designa qualquer lógica que incorpore conceitos probabilísticos num sistema lógico formal. Nesta dissertacção o principal foco de estudo e uma lógica probabilística (designada por Lógica Proposicional Probabilística Exógena), que tem por base a Lógica Proposicional Clássica. São trabalhados sobre essa lógica probabilística a síntaxe, a semântica e um cálculo de Hilbert, provando-se diversos resultados clássicos de Teoria de Probabilidade no contexto da EPPL. São também estudadas duas propriedades muito importantes de um sistema lógico - correcção e completude. Prova-se a correcção da EPPL da forma usual, e a completude fraca recorrendo a um algoritmo de satisfazibilidade de uma fórmula da EPPL. Serão também considerados na EPPL conceitos de outras lógicas probabilísticas (incerteza e probabilidades intervalares) e Teoria de Probabilidades (condicionais e independência).
The term Probabilistic Logic generally refers to any logic that incorporates probabilistic concepts in a formal logic system. In this dissertation, the main focus of study is a probabilistic logic (called Exogenous Probabilistic Propo- sitional Logic), which is based in the Classical Propositional Logic. There will be introduced, for this probabilistic logic, its syntax, semantics and a Hilbert calculus, proving some classical results of Probability Theory in the context of EPPL. Moreover, there will also be studied two important properties of a logic system - soundness and completeness. We prove the EPPL soundness in a standard way, and weak completeness using a satis ability algorithm for a formula of EPPL. It will be considered in EPPL concepts of other probabilistic logics (uncertainty and intervalar probability) and of Probability Theory (independence and conditional).

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VIEIRA, BRUNO LOPES. "EXTENDING PROPOSITIONAL DYNAMIC LOGIC FOR PETRI NETS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2014. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=24052@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE EXCELENCIA ACADEMICA
Lógica Proposicional Dinâmica (PDL) é um sistema lógico multi-modal utilizada para especificar e verificar propriedades em programas sequenciais. Redes de Petri são um formalismo largamente utilizado na especificação de sistemas concorrentes e possuem uma interpretação gráfica bastante intuitiva. Neste trabalho apresentam-se extensões da Lógica Proposicional Dinâmica onde os programas são substituídos por Redes de Petri. Define-se uma codificação composicional para as Redes de Petri através de redes básicas, apresentando uma semântica composicional. Uma axiomatização é definida para a qual o sistema é provado ser correto, e completo em relação à semântica proposta. Três Lógicas Dinâmicas são apresentadas: uma para efetuar inferências sobre Redes de Petri Marcadas ordinárias e duas para inferências sobre Redes de Petri Estocásticas marcadas, possibilitando a modelagem de cenários mais complexos. Alguns sistemas dedutivos para essas lógicas são apresentados. A principal vantagem desta abordagem concerne em possibilitar efetuar inferências sobre Redes de Petri [Estocásticas] marcadas sem a necessidade de traduzí-las a outros formalismos.
Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyze concurrent programs with a very intuitive graphical representation. In this work, we propose some extensions of Propositional Dynamic Logic for reasoning about Petri Nets. We define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Then we present an axiomatization and prove completeness regarding our semantics. Three versions of Dynamic Logics to reasoning with Petri Nets are presented: one of them for ordinary Marked Petri Nets and two for Marked Stochastic Petri Nets yielding to the possibility of model more complex scenarios. Some deductive systems are presented. The main advantage of our approach is that we can reason about [Stochastic] Petri Nets using our Dynamic Logic and we do not need to translate it into other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.

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Lee, Chen-Hsiu. "A tabular propositional logic: and/or Table Translator." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2409.

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The goal of this project is to design a tool to help users translate any logic statement into Disjunctive Normal Form and present the result as an AND/OR TABLE, which makes the logic relation easier to express by using a two-dimensional grid of values or expressions. This tool is implemented through a web-based and Java-based application. Thus, the user can utilize this tool via World Wide Web.

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Mitrović, Moreno. "Morphosyntactic atoms of propositional logic : (a philo-logical programme)." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709276.

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Boskovitz, Agnes, and abvi@webone com au. "Data Editing and Logic: The covering set method from the perspective of logic." The Australian National University. Research School of Information Sciences and Engineering, 2008. http://thesis.anu.edu.au./public/adt-ANU20080314.163155.

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Errors in collections of data can cause significant problems when those data are used. Therefore the owners of data find themselves spending much time on data cleaning. This thesis is a theoretical work about one part of the broad subject of data cleaning - to be called the covering set method. More specifically, the covering set method deals with data records that have been assessed by the use of edits, which are rules that the data records are supposed to obey. The problem solved by the covering set method is the error localisation problem, which is the problem of determining the erroneous fields within data records that fail the edits. In this thesis I analyse the covering set method from the perspective of propositional logic. I demonstrate that the covering set method has strong parallels with well-known parts of propositional logic. The first aspect of the covering set method that I analyse is the edit generation function, which is the main function used in the covering set method. I demonstrate that the edit generation function can be formalised as a logical deduction function in propositional logic. I also demonstrate that the best-known edit generation function, written here as FH (standing for Fellegi-Holt), is essentially the same as propositional resolution deduction. Since there are many automated implementations of propositional resolution, the equivalence of FH with propositional resolution gives some hope that the covering set method might be implementable with automated logic tools. However, before any implementation, the other main aspect of the covering set method must also be formalised in terms of logic. This other aspect, to be called covering set correctibility, is the property that must be obeyed by the edit generation function if the covering set method is to successfully solve the error localisation problem. In this thesis I demonstrate that covering set correctibility is a strengthening of the well-known logical properties of soundness and refutation completeness. What is more, the proofs of the covering set correctibility of FH and of the soundness / completeness of resolution deduction have strong parallels: while the proof of soundness / completeness depends on the reduction property for counter-examples, the proof of covering set correctibility depends on the related lifting property. In this thesis I also use the lifting property to prove the covering set correctibility of the function defined by the Field Code Forest Algorithm. In so doing, I prove that the Field Code Forest Algorithm, whose correctness has been questioned, is indeed correct. The results about edit generation functions and covering set correctibility apply to both categorical edits (edits about discrete data) and arithmetic edits (edits expressible as linear inequalities). Thus this thesis gives the beginnings of a theoretical logical framework for error localisation, which might give new insights to the problem. In addition, the new insights will help develop new tools using automated logic tools. What is more, the strong parallels between the covering set method and aspects of logic are of aesthetic appeal.

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QUILLEN, KEITH RAYMOND. "PROPOSITIONAL ATTITUDES AND PSYCHOLOGICAL EXPLANATION (MIND, MENTAL)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188053.

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Propositional attitudes, states like believing, desiring, intending, etc., have played a central role in the articulation of many of our major theories, both in philosophy and the social sciences. Until relatively recently, psychology was a prominent entry on the list of social sciences in which propositional attitudes occupied center stage. In this century, though, behaviorists began to make a self-conscious effort to expunge "mentalistic" notions from their theorizing. Behaviorism has failed. Psychology therefore is again experiencing "formative years," and two themes have caught the interest of philosophers. The first is that psychological theories evidently must exploit a vast array of relations obtaining among internal states. The second is that the use of mentalistic idioms seems to be explicit again in much of current theorizing. These two observations have led philosophers to wonder about the probable as well as the proper role of propositional attitudes in future psychological theories. Some philosophers wonder, in particular, about the role of the contents of propositional attitudes in the forthcoming theories. Their strategy is in part to discern what sorts of theory psychologists now will want to construct, and then discern what role propositional attitude contents might play in theories of those sorts. I consider here two sorts of theory, what I call minimal functional theories and what is known as propositional attitude psychology. I outline these two kinds of theory, and show how each defines a role for contents. Contents are ultimately eliminable in minimal functional theories. Although they play an apparently ineliminable role in propositional attitude psychology, they do so at an apparent cost. Propositional attitude psychology does not seem to accommodate a certain methodological principle, a principle of individualism in psychology, which is endorsed even by some of the philosophers most enamored of the approach. Such philosophers have two options: they can attempt to show that the conflict between the approach and the principle is not genuine, or they can reject the principle. I argue that the conflict is real, and recommend a qualified rejections of the principle.

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Favro, Giordano <1985&gt. "Algebraic structures for the lambda calculus and the propositional logic." Doctoral thesis, Università Ca' Foscari Venezia, 2015. http://hdl.handle.net/10579/8333.

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Nella prima parte della tesi definiamo due famiglie di insiemi, Mn e Gn, dove n è un indice sui naturali, costituiti da termini muti detti rispettivamente restricted regular mute e regular mute e definiti induttivamente. Proviamo inoltre che gli insiemi Mn sono graph easy, ovvero che per ogni termine chiuso t esiste un graph model che eguaglia t a tutti gli elementi di Mn. Nella seconda parte introduciamo le factor algebras su tipi del primo ordine. Mostriamo come possano essere usate come controparte algebrica per le strutture su tipi del primo ordine. Mostriamo che questa traduzione si estende a formule ed equazioni fra termini e che queste traduzioni hanno un significato semantico. Utilizzando questi risultati, possiamo studiare la logica del primo ordine tramite tecniche algebriche. Costruiamo quindi un calcolo algebrico per la logica proposizionale basato sugli assiomi della varietà generata dalle factor algebras sul tipo della logica proposizionale. Forniamo inoltre un sistema di riscrittura confluente e terminante per il calcolo. Inoltre analizziamo le proprietà algebriche di base delle factor algebras su tipi del primo ordine.

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Walton, Matthew. "First-order lax logic : a framework for abstraction, constraints and refinement." Thesis, University of Sheffield, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299599.

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Gore, Rajeev. "Cut-free sequent and tableau systems for propositional normal modal logics." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239668.

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Namasivayam, Gayathri. "ON SIMPLE BUT HARD RANDOM INSTANCES OF PROPOSITIONAL THEORIES AND LOGIC PROGRAMS." UKnowledge, 2011. http://uknowledge.uky.edu/gradschool_diss/132.

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In the last decade, Answer Set Programming (ASP) and Satisfiability (SAT) have been used to solve combinatorial search problems and practical applications in which they arise. In each of these formalisms, a tool called a solver is used to solve problems. A solver takes as input a specification of the problem – a logic program in the case of ASP, and a CNF theory for SAT – and produces as output a solution to the problem. Designing fast solvers is important for the success of this general-purpose approach to solving search problems. Classes of instances that pose challenges to solvers can help in this task. In this dissertation we create challenging yet simple benchmarks for existing solvers in ASP and SAT.We do so by providing models of simple logic programs as well as models of simple CNF theories. We then randomly generate logic programs as well as CNF theories from these models. Our experimental results show that computing answer sets of random logic programs as well as models of random CNF theories with carefully chosen parameters is hard for existing solvers. We generate random logic programs with 2-literals, and our experiments show that it is hard for ASP solvers to obtain answer sets of purely negative and constraint-free programs, indicating the importance of these programs in the development of ASP solvers. An easy-hard-easy pattern emerges as we compute the average number of choice points generated by ASP solvers on randomly generated 2-literal programs with an increasing number of rules. We provide an explanation for the emergence of this pattern in these programs. We also theoretically study the probability of existence of an answer set for sparse and dense 2-literal programs. We consider simple classes of mixed Horn formulas with purely positive 2- literal clauses and purely negated Horn clauses. First we consider a class of mixed Horn formulas wherein each formula has m 2-literal clauses and k-literal negated Horn clauses. We show that formulas that are generated from the phase transition region of this class are hard for complete SAT solvers. The second class of Mixed Horn Formulas we consider are obtained from completion of a certain class of random logic programs. We show the appearance of an easy-hard-easy pattern as we generate formulas from this class with increasing numbers of clauses, and that the formulas generated in the hard region can be used as benchmarks for testing incomplete SAT solvers.

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Books on the topic "Propositional logic"

Fairtlough, Matt. Propositional lax logic. Sheffield: University of Sheffield, Dept. of Computer Science, 1995.

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G, Lycan William, and Pospesel Mark, eds. Propositional Logic (Introduction to Logic). 3rd ed. Upper Saddle River, N.J: Prentice Hall, 2000.

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G, Lycan William, ed. Propositional Logic (Introduction to Logic). 3rd ed. Upper Saddle River, N.J: Prentice Hall, 1998.

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Gisle, Andersen, and Fretheim Thorstein, eds. Pragmatic markers and propositional attitude. Amsterdam: J. Benjamins Pub., 2000.

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Dahllöf, Mats. On the semantics of propositional attitude reports. Göteborg, Sweden: Göteborg University, Dept. of Linguistics, 1995.

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Hudson, Stephen. Demonstration software in propositional logic. Oxford: Oxford Brookes University, 2001.

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Theodor, Lettman, ed. Propositional logic: Deduction and algorithms. Cambridge [England]: Cambridge University Press, 1999.

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Li, Wei, and Yuefei Sui. R-Calculus, IV: Propositional Logic. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-19-8633-8.

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Epstein, Richard L. The Semantic Foundations of Logic Volume 1: Propositional Logics. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0525-2.

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Poggiolesi, Francesca. Gentzen Calculi for Modal Propositional Logic. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-90-481-9670-8.

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Book chapters on the topic "Propositional logic"

Nerode, Anil, and Richard A. Shore. "Propositional Logic." In Logic for Applications, 7–79. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-0649-1_2.

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Anshakov, Oleg M., and Tamás Gergely. "Propositional Logic." In Cognitive Research, 73–92. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-68875-4_7.

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Hall, Cordelia, and John O’Donnell. "Propositional Logic." In Discrete Mathematics Using a Computer, 35–87. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-3657-6_2.

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van Dalen, Dirk. "Propositional Logic." In Universitext, 5–52. London: Springer London, 2013. http://dx.doi.org/10.1007/978-1-4471-4558-5_2.

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Fitting, Melvin. "Propositional Logic." In First-Order Logic and Automated Theorem Proving, 8–35. New York, NY: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4684-0357-2_2.

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Pace, Gordon J. "Propositional Logic." In Mathematics of Discrete Structures for Computer Science, 9–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-29840-0_2.

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Vingron, Shimon P. "Propositional Logic." In Switching Theory, 89–100. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-10174-2_9.

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Fitting, Melvin. "Propositional Logic." In First-Order Logic and Automated Theorem Proving, 9–39. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-2360-3_2.

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Liu, Shaoying. "Propositional Logic." In Formal Engineering for Industrial Software Development, 21–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-07287-5_2.

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Zeugmann, Thomas, Pascal Poupart, James Kennedy, Xin Jin, Jiawei Han, Lorenza Saitta, Michele Sebag, et al. "Propositional Logic." In Encyclopedia of Machine Learning, 812. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-30164-8_679.

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Conference papers on the topic "Propositional logic"

Console, Marco, Paolo Guagliardo, and Leonid Libkin. "Do We Need Many-valued Logics for Incomplete Information?" In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/851.

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One of the most common scenarios of handling incomplete information occurs in relational databases. They describe incomplete knowledge with three truth values, using Kleene's logic for propositional formulae and a rather peculiar extension to predicate calculus. This design by a committee from several decades ago is now part of the standard adopted by vendors of database management systems. But is it really the right way to handle incompleteness in propositional and predicate logics? Our goal is to answer this question. Using an epistemic approach, we first characterize possible levels of partial knowledge about propositions, which leads to six truth values. We impose rationality conditions on the semantics of the connectives of the propositional logic, and prove that Kleene's logic is the maximal sublogic to which the standard optimization rules apply, thereby justifying this design choice. For extensions to predicate logic, however, we show that the additional truth values are not necessary: every many-valued extension of first-order logic over databases with incomplete information represented by null values is no more powerful than the usual two-valued logic with the standard Boolean interpretation of the connectives. We use this observation to analyze the logic underlying SQL query evaluation, and conclude that the many-valued extension for handling incompleteness does not add any expressiveness to it.

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Ma, Minghui, and Katsuhiko Sano. "On Extensions of Basic Propositional Logic." In 13th Asian Logic Conference. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814678001_0011.

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Guller, Dušan. "Hyperresolution for Propositional Product Logic." In 8th International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0006044300300041.

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Bo, Chen, Wu Cheng, Zhang Bing, Ma Changhui, and Sui Yuefei. "Quantified Propositional Logic and Translations." In 2017 13th International Conference on Semantics, Knowledge and Grids (SKG). IEEE, 2017. http://dx.doi.org/10.1109/skg.2017.00010.

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Chen, Bo, Kang Zhao, Bing Zhang, Cheng Wu, Linlin Ma, Changhui Ma, and Yuefei Sui. "The B5-Modalized Propositional Logic." In 2019 15th International Conference on Semantics, Knowledge and Grids (SKG). IEEE, 2019. http://dx.doi.org/10.1109/skg49510.2019.00035.

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Benevides, Mario Folhadela, and Anna Moreira De Oliveira. "Propositional Dynamic Logic for Planning." In Workshop Brasileiro de Lógica. Sociedade Brasileira de Computação - SBC, 2020. http://dx.doi.org/10.5753/wbl.2020.11454.

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This paper presents an on going work on Propositional Dynamic Logic PDL in which atomic programs are STRIPS actions. We think that this new framework is appropriate to reasoning about actions and plans when dealing with planning problem. Unlike, PDL atomic programs, STRIPS actions have pre-conditions and post-conditions. We propose a novel operator of action composition that takes in account the features of STRIPS actions. We propose an axiomatization and prove its soundness. Completeness, decidability and computational complexity are left as future work.

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Herzig, Andreas, Frédéric Maris, and Elise Perrotin. "A Dynamic Epistemic Logic with Finite Iteration and Parallel Composition." In 18th International Conference on Principles of Knowledge Representation and Reasoning {KR-2021}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/kr.2021/68.

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Existing dynamic epistemic logics combine standard epistemic logic with a restricted version of dynamic logic. Instead, we here combine a restricted epistemic logic with a rich version of dynamic logic. The epistemic logic is based on `knowing-whether' operators and basically disallows disjunctions and conjunctions in their scope; it moreover captures `knowing-what'. The dynamic logic has not only all the standard program operators of Propositional Dynamic Logic, but also parallel composition as well as an operator of inclusive nondeterministic composition; its atomic programs are assignments of propositional variables. We show that the resulting dynamic epistemic logic is powerful enough to capture several kinds of sequential and parallel planning, and so both in the unbounded and in the finite horizon version.

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Grossi, Davide, Emiliano Lorini, and François Schwarzentruber. "The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/710.

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We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

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Codara, Pietro, Ottavio M. D'Antona, and Vincenzo Marra. "Propositional Gödel Logic and Delannoy Paths." In 2007 IEEE International Fuzzy Systems Conference. IEEE, 2007. http://dx.doi.org/10.1109/fuzzy.2007.4295542.

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Chang, Zhiyan, Yang Xu, Jiajun Lai, and Xiqing Long. "A Comparison between Lattice-Valued Propositional Logic LP(X) and Gradational Lattice-Valued Propositional Logic Lvpl." In International Conference on Intelligent Systems and Knowledge Engineering 2007. Paris, France: Atlantis Press, 2007. http://dx.doi.org/10.2991/iske.2007.268.

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Reports on the topic "Propositional logic"

Strichman, Ofer, Sanjit A. Seshia, and Randal E. Bryant. Reducing Separation Formulas to Propositional Logic. Fort Belvoir, VA: Defense Technical Information Center, April 2003. http://dx.doi.org/10.21236/ada461197.

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Lutz, Carsten, and Ulrike Sattler. The Complexity of Reasoning with Boolean Modal Logics (Extended Version). Aachen University of Technology, 1999. http://dx.doi.org/10.25368/2022.105.

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Since Modal Logics are an extension of Propositional Logic, they provide Boolean operators for constructing complex formulae. However, most Modal Logics do not admit Boolean operators for constructing complex modal parameters to be used in the box and diamond operators. This asymmetry is not present in Boolean Modal Logics, in which box and diamond quantify over arbitrary Boolean combinations of atomic model parameters.

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Lutz, Carsten, and Dirk Walther. PDL with Negation of Atomic Programs. Technische Universität Dresden, 2003. http://dx.doi.org/10.25368/2022.129.

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Propositional dynamic logic (PDL) is one of the most succesful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, it is long-known that reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata.

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Baader, Franz, and Marcel Lippmann. Runtime Verification Using a Temporal Description Logic Revisited. Technische Universität Dresden, 2014. http://dx.doi.org/10.25368/2022.203.

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Formulae of linear temporal logic (LTL) can be used to specify (wanted or unwanted) properties of a dynamical system. In model checking, the system’s behaviour is described by a transition system, and one needs to check whether all possible traces of this transition system satisfy the formula. In runtime verification, one observes the actual system behaviour, which at any point in time yields a finite prefix of a trace. The task is then to check whether all continuations of this prefix to a trace satisfy (violate) the formula. More precisely, one wants to construct a monitor, i.e., a finite automaton that receives the finite prefix as input and then gives the right answer based on the state currently reached. In this paper, we extend the known approaches to LTL runtime verification in two directions. First, instead of propositional LTL we use the more expressive temporal logic ALC-LTL, which can use axioms of the Description Logic (DL) ALC instead of propositional variables to describe properties of single states of the system. Second, instead of assuming that the observed system behaviour provides us with complete information about the states of the system, we assume that states are described in an incomplete way by ALC-knowledge bases. We show that also in this setting monitors can effectively be constructed. The (double-exponential) size of the constructed monitors is in fact optimal, and not higher than in the propositional case. As an auxiliary result, we show how to construct Büchi automata for ALC-LTL-formulae, which yields alternative proofs for the known upper bounds of deciding satisfiability in ALC-LTL.

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Borgwardt, Stefan, Marcel Lippmann, and Veronika Thost. Reasoning with Temporal Properties over Axioms of DL-Lite. Technische Universität Dresden, 2014. http://dx.doi.org/10.25368/2022.208.

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Recently, a lot of research has combined description logics (DLs) of the DL-Lite family with temporal formalisms. Such logics are proposed to be used for situation recognition and temporalized ontology-based data access. In this report, we consider DL-Lite-LTL, in which axioms formulated in a member of the DL-Lite family are combined using the operators of propositional linear-time temporal logic (LTL). We consider the satisfiability problem of this logic in the presence of so-called rigid symbols whose interpretation does not change over time. In contrast to more expressive temporalized DLs, the computational complexity of this problem is the same as for LTL, even w.r.t. rigid symbols.

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Peñaloza, Rafael, and Barış Sertkaya. On the Complexity of Axiom Pinpointing in Description Logics. Technische Universität Dresden, 2009. http://dx.doi.org/10.25368/2022.173.

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We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.

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Baader, Franz, Stefan Borgwardt, and Marcel Lippmann. On the Complexity of Temporal Query Answering. Technische Universität Dresden, 2013. http://dx.doi.org/10.25368/2022.191.

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Ontology-based data access (OBDA) generalizes query answering in databases towards deduction since (i) the fact base is not assumed to contain complete knowledge (i.e., there is no closed world assumption), and (ii) the interpretation of the predicates occurring in the queries is constrained by axioms of an ontology. OBDA has been investigated in detail for the case where the ontology is expressed by an appropriate Description Logic (DL) and the queries are conjunctive queries. Motivated by situation awareness applications, we investigate an extension of OBDA to the temporal case. As query language we consider an extension of the well-known propositional temporal logic LTL where conjunctive queries can occur in place of propositional variables, and as ontology language we use the prototypical expressive DL ALC. For the resulting instance of temporalized OBDA, we investigate both data complexity and combined complexity of the query entailment problem.

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Lutz, Carsten. PDL with Intersection and Converse is Decidable. Technische Universität Dresden, 2005. http://dx.doi.org/10.25368/2022.148.

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In its many guises and variations, propositional dynamic logic (PDL) plays an important role in various areas of computer science such as databases, artificial intelligence, and computer linguistics. One relevant and powerful variation is ICPDL, the extension of PDL with intersection and converse. Although ICPDL has several interesting applications, its computational properties have never been investigated. In this paper, we prove that ICPDL is decidable by developing a translation to the monadic second order logic of infinite trees. Our result has applications in information logic, description logic, and epistemic logic. In particular, we solve a long-standing open problem in information logic. Another virtue of our approach is that it provides a decidability proof that is more transparent than existing ones for PDL with intersection (but without converse).

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Borgwardt, Stefan, and Veronika Thost. Temporal Query Answering in DL-Lite with Negation. Technische Universität Dresden, 2015. http://dx.doi.org/10.25368/2022.221.

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Ontology-based query answering augments classical query answering in databases by adopting the open-world assumption and by including domain knowledge provided by an ontology. We investigate temporal query answering w.r.t. ontologies formulated in DL-Lite, a family of description logics that captures the conceptual features of relational databases and was tailored for efficient query answering. We consider a recently proposed temporal query language that combines conjunctive queries with the operators of propositional linear temporal logic (LTL). In particular, we consider negation in the ontology and query language, and study both data and combined complexity of query entailment.

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Baader, Franz, Stefan Borgwardt, and Barbara Morawska. SAT Encoding of Unification in ELHR+ w.r.t. Cycle-Restricted Ontologies. Technische Universität Dresden, 2012. http://dx.doi.org/10.25368/2022.186.

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Unification in Description Logics has been proposed as an inference service that can, for example, be used to detect redundancies in ontologies. For the Description Logic EL, which is used to define several large biomedical ontologies, unification is NP-complete. An NP unification algorithm for EL based on a translation into propositional satisfiability (SAT) has recently been presented. In this report, we extend this SAT encoding in two directions: on the one hand, we add general concept inclusion axioms, and on the other hand, we add role hierarchies (H) and transitive roles (R+). For the translation to be complete, however, the ontology needs to satisfy a certain cycle restriction. The SAT translation depends on a new rewriting-based characterization of subsumption w.r.t. ELHR+-ontologies.

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