Propositional Logic: SAT Solvers

2012 ◽  
pp. 111-129
Author(s):  
Mordechai Ben-Ari
Keyword(s):  
Propositional Logic ◽  
Sat Solvers

scholarly journals A Theory of Satisfiability-Preserving Proofs in SAT Solving

10.29007/tc7q ◽  
2018 ◽  
Author(s):  
Adrián Rebola-Pardo ◽  
Martin Suda
Keyword(s):  
Propositional Logic ◽  
Logical Truth ◽  
Point Of View ◽  
Traditional View ◽  
Satisfiability Problem ◽  
Sat Solving ◽  
Sat Solvers ◽  
Proof Systems ◽  
Meta Level

We study the semantics of propositional interference-based proof systems such as DRAT and DPR. These are characterized by modifying a CNF formula in ways that preserve satisfiability but not necessarily logical truth. We propose an extension of propositional logic called overwrite logic with a new construct which captures the meta-level reasoning behind interferences. We analyze this new logic from the point of view of expressivity and complexity, showing that while greater expressivity is achieved, the satisfiability problem for overwrite logic is essentially as hard as SAT, and can be reduced in a way that is well-behaved for modern SAT solvers. We also show that DRAT and DPR proofs can be seen as overwrite logic proofs which preserve logical truth. This much stronger invariant than the mere satisfiability preservation maintained by the traditional view gives us better understanding on these practically important proof systems. Finally, we showcase this better understanding by finding intrinsic limitations in interference-based proof systems.

scholarly journals Extended Resolution as Certificates for Propositional Logic

10.29007/vrpk ◽  
2018 ◽  
Author(s):  
Chantal Keller
Keyword(s):  
Propositional Logic ◽  
Proof Assistants ◽  
Sat Solvers

When checking answers coming from automatic provers, or when skeptically integrating them into proof assistants, a major problem is the wide variety of formats of certificates, which forces to write lots of different checkers. In this paper, we propose to use the extended resolution as a common format for every propositional prover. To be able to do this, we detail two algorithms transforming proofs computed respectively by tableaux provers and provers based on {\bdd}s into this format. Since this latter is already implemented for SAT solvers, it is now possible for the three most common propositional provers to share the same certificates.

Hilbert-style proof Calculus for Propositional Logic in ABC notation

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Propositional Logic ◽  
Inference Rule ◽  
Modus Ponens ◽  
Axiomatic System ◽  
First Contact

All nine axioms and a single inference rule of logic (Modus Ponens) within the Hilbert axiomatic system are presented using capital letters (ABC) in order to familiarize the beginner student in hers/his first contact with the topic.

Reducing Separation Formulas to Propositional Logic

2003 ◽  
Author(s):  
Ofer Strichman ◽  
Sanjit A. Seshia ◽  
Randal E. Bryant
Keyword(s):  
Propositional Logic

scholarly journals Extensions in graph normal form

2020 ◽  
Author(s):  
Michał Walicki
Keyword(s):  
Normal Form ◽  
Fixed Points ◽  
Propositional Logic ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Special Cases

Abstract Graph normal form, introduced earlier for propositional logic, is shown to be a normal form also for first-order logic. It allows to view syntax of theories as digraphs, while their semantics as kernels of these digraphs. Graphs are particularly well suited for studying circularity, and we provide some general means for verifying that circular or apparently circular extensions are conservative. Traditional syntactic means of ensuring conservativity, like definitional extensions or positive occurrences guaranteeing exsitence of fixed points, emerge as special cases.

scholarly journals ACO with Intuitionistic Fuzzy Pheromone Updating Applied on Multiple-Constraint Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1456
Author(s):  
Stefka Fidanova ◽  
Krassimir Todorov Atanassov
Keyword(s):  
Decision Making ◽  
Knapsack Problem ◽  
Propositional Logic ◽  
Optimization Problems ◽  
Real Life ◽  
Combinatorial Optimization Problems ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Multiple Constraint

Some of industrial and real life problems are difficult to be solved by traditional methods, because they need exponential number of calculations. As an example, we can mention decision-making problems. They can be defined as optimization problems. Ant Colony Optimization (ACO) is between the best methods, that solves combinatorial optimization problems. The method mimics behavior of the ants in the nature, when they look for a food. One of the algorithm parameters is called pheromone, and it is updated every iteration according quality of the achieved solutions. The intuitionistic fuzzy (propositional) logic was introduced as an extension of Zadeh’s fuzzy logic. In it, each proposition is estimated by two values: degree of validity and degree of non-validity. In this paper, we propose two variants of intuitionistic fuzzy pheromone updating. We apply our ideas on Multiple-Constraint Knapsack Problem (MKP) and compare achieved results with traditional ACO.

scholarly journals Deduction in Non-Fregean Propositional Logic SCI

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 115 ◽  
Author(s):  
Joanna Golińska-Pilarek ◽  
Magdalena Welle
Keyword(s):  
Propositional Logic ◽  
Sequent Calculus ◽  
Classical Propositional Logic ◽  
Tableau System ◽  
Soundness And Completeness

We study deduction systems for the weakest, extensional and two-valued non-Fregean propositional logic SCI . The language of SCI is obtained by expanding the language of classical propositional logic with a new binary connective ≡ that expresses the identity of two statements; that is, it connects two statements and forms a new one, which is true whenever the semantic correlates of the arguments are the same. On the formal side, SCI is an extension of classical propositional logic with axioms characterizing the identity connective, postulating that identity must be an equivalence and obey an extensionality principle. First, we present and discuss two types of systems for SCI known from the literature, namely sequent calculus and a dual tableau-like system. Then, we present a new dual tableau system for SCI and prove its soundness and completeness. Finally, we discuss and compare the systems presented in the paper.

Masking Circuit Faults and Trojan Circuit Injections Using Sat Solvers

2021 ◽  
Vol 63 (12) ◽  
pp. 2178-2188
Author(s):  
A. Yu. Маtrosova ◽  
V. А. Provkin ◽  
V. Z. Tychinskiy ◽  
Е. А. Nikolaeva ◽  
G. G. Goshin
Keyword(s):  
Sat Solvers
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