Reasoning with Propositional Logic: From SAT Solvers to Knowledge Compilation

2020 ◽  
pp. 115-152
Author(s):  
Laurent Simon
Keyword(s):  
Propositional Logic ◽  
Knowledge Compilation ◽  
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.

KNOWLEDGE BASE REFORMATION: PREPARING FIRST-ORDER THEORIES FOR EFFICIENT PROPOSITIONAL REASONING

2000 ◽  
Vol 14 (01) ◽  
pp. 35-57 ◽  
Author(s):  
HELMUT PRENDINGER ◽  
MITSURU ISHIZUKA ◽  
GERHARD SCHURZ
Keyword(s):  
Knowledge Base ◽  
Propositional Logic ◽  
Knowledge Compilation ◽  
First Order ◽  
Order Language

We present an approach to knowledge compilation that transforms a function-free first-order Horn knowledge base to propositional logic. This form of compilation is important since the most efficient reasoning methods are defined for propositional logic, while knowledge is most conveniently expressed within a first-order language. To obtain compact propositional representations, we employ techniques from (ir)relevance reasoning as well as theory transformation via unfold/fold transformations. Application areas include diagnosis, planning, and vision. Preliminary experiments with a hypothetical reasoner indicate that our method may yield significant speed-ups.

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.

scholarly journals Knowledge compilation of logic programs using approximation fixpoint theory

2015 ◽  
Vol 15 (4-5) ◽  
pp. 464-480 ◽  
Author(s):  
BART BOGAERTS ◽  
GUY VAN DEN BROECK
Keyword(s):  
Propositional Logic ◽  
Default Logic ◽  
Knowledge Compilation ◽  
Auxiliary Variables ◽  
Logic Programs ◽  
Autoepistemic Logic ◽  
Recent Advances ◽  
Logical Equivalence ◽  
General Logic

AbstractRecent advances in knowledge compilation introduced techniques to compilepositivelogic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited tonegation-freeprograms. In this paper, we show how to extend it to general logic programs under the well-founded semantics.We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks.

Knowledge-Based Description Logic ALCO Knowledge Compiled Algorithm to Determine Consistency

2012 ◽  
Vol 487 ◽  
pp. 347-351
Author(s):  
Ya Qiong Jiang ◽  
Jun Wang
Keyword(s):  
Normal Form ◽  
Knowledge Base ◽  
Propositional Logic ◽  
Description Logic ◽  
Knowledge Bases ◽  
Knowledge Compilation ◽  
Knowledge Based ◽  
Common Technique ◽  
Compilation Techniques

Knowledge compilation is a common technique for propositional logic knowledge bases. A given knowledge base is transformed into a normal form, for which reasoning can be answered efficiently. The precompilation of description logic knowledge base is important for reasoning and services of description logic. This paper gives precompilation about the description logic ALCO TBox based on knowledge compilation techniques, for which the consistency of TBox can be determined.

scholarly journals Prime Implicates and Prime Implicants: From Propositional to Modal Logic

2009 ◽  
Vol 36 ◽  
pp. 71-128 ◽  
Author(s):  
M. Bienvenu
Keyword(s):  
Artificial Intelligence ◽  
Modal Logic ◽  
Propositional Logic ◽  
Description Logic ◽  
Recognition Task ◽  
Abductive Reasoning ◽  
Upper And Lower Bounds ◽  
Knowledge Compilation ◽  
Prime Implicants ◽  
Computational Properties

Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be appropriately extended from propositional logic to the modal logic K. We begin the paper by considering a number of potential definitions of clauses and terms for K. The different definitions are evaluated with respect to a set of syntactic, semantic, and complexity-theoretic properties characteristic of the propositional definition. We then compare the definitions with respect to the properties of the notions of prime implicates and prime implicants that they induce. While there is no definition that perfectly generalizes the propositional notions, we show that there does exist one definition which satisfies many of the desirable properties of the propositional case. In the second half of the paper, we consider the computational properties of the selected definition. To this end, we provide sound and complete algorithms for generating and recognizing prime implicates, and we show the prime implicate recognition task to be PSPACE-complete. We also prove upper and lower bounds on the size and number of prime implicates. While the paper focuses on the logic K, all of our results hold equally well for multi-modal K and for concept expressions in the description logic ALC.

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
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