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Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach
International Symposium on Foundations of Information and Knowledge Systems, 2008 V. Efstathiou, A. Hunter
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Classical and Fuzzy Concepts in Mathematical Logic and Applications
, 2022Preliminaries of "Naive" Mathematical Logic PART I. Propositional Logic The Formal Language of Propositional Logic The Formal Language Lo of Propositional Logic Using Parentheses The Formal Language Lo of Propositional Logic without Parentheses (Polish ...
M. Reghiş, E. Roventa
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2001
Abstract Classical propositional logic has associated with it a number of different algebraic log ics, which we will call Frege logic, Boolean logic, and unital Boolean logic. Although these logics are characterized by different classes of logical matrices, as we will see later, they are all strongly equivalent, which is to say that they
J Michael Dunn, Gary M Hardegree
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Abstract Classical propositional logic has associated with it a number of different algebraic log ics, which we will call Frege logic, Boolean logic, and unital Boolean logic. Although these logics are characterized by different classes of logical matrices, as we will see later, they are all strongly equivalent, which is to say that they
J Michael Dunn, Gary M Hardegree
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Teaching Semantic Tableaux Method for Propositional Classical Logic with a CAS
The International Journal for Technology in Mathematics Education, 2015Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem.
G. Aguilera–Venegas +3 more
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A note on decidability of variables in intuitionistic propositional logic
Mathematical Logic Quarterly, 2018An answer to the following question is presented: given a proof Γ⊢A in classical propositional logic, for what small set of propositional variables p does it suffice to add all the formulae p∨¬p to Γ in order to intuitionistically prove A? This answer is
Katsumasa Ishii
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Deciding intuitionistic propositional logic via translation into classical logic
1997We present a technique that efficiently translates prepositional intuitionistic formulas into propositional classical formulas. This technique allows the use of arbitrary classical theorem provers for deciding the intuitionistic validity of a given propositional formula. The translation is based on the constructive description of a finite counter-model
Daniel S. Korn, Christoph Kreitz
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tascpl: TAS Solver for Classical Propositional Logic
2004We briefly overview the most recent improvements we have incorporated to the existent implementations of the TAS methodology, the simplified Δ-tree representation of formulas in negation normal form. This new representation allows for a better description of the reduction strategies, in that considers only those occurrences of literals which are ...
M. Ojeda-Aciego, A. Valverde
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Axiomatic Rejection for Classical Propositional Logic
1996Axiomatic rejection is a method to recursively enumerate all the formulas not provable in the given formal system by way of a recursive set of axioms and rules, not necessarily finite.
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Classical Gentzen-type Methods in Propositional Many-valued Logics
Proceedings 31st IEEE International Symposium on Multiple-Valued Logic, 2002A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzen-type system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property.
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A Classical Propositional Logic for Reasoning About Reversible Logic Circuits
2016We propose a syntactic representation of reversible logic circuits in their entirety, based on Feynman's control interpretation of Toffoli's reversible gate set. A pair of interacting proof calculi for reasoning about these circuits is presented, based on classical propositional logic and monoidal structure, and a natural order-theoretic structure is ...
Axelsen, Holger Bock +2 more
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