Refutation Systems: An Overview and Some Applications to Philosophical Logics

2020 ◽  
pp. 173-197 ◽  
Author(s):  
Valentin Goranko ◽  
Gabriele Pulcini ◽  
Tomasz Skura
Keyword(s):  
Refutation Systems

scholarly journals Hybrid Deduction-Refutation Systems for FDE-Based Logics

2021 ◽  
Vol 18 (6) ◽  
pp. 599-615
Author(s):  
Eoin Moore
Keyword(s):  
Hybrid Systems ◽  
Hybrid System ◽  
Classical Logic ◽  
First Degree Entailment ◽  
Refutation Systems

Hybrid deduction-refuation systems are presented for four first-degree entailment based logics. The hybrid systems are shown to be deductively and refutationally sound with respect to their logics. The proofs of completeness are presented in a uniform way. The paper builds on work by Goranko, who presented a deductively and refutationally sound and complete hybrid system for classical logic.

scholarly journals Non-clausal Redundancy Properties

2021 ◽  
pp. 252-272
Author(s):  
Lee A. Barnett ◽  
Armin Biere
Keyword(s):  
State Of The Art ◽  
Binary Decision Diagrams ◽  
Gaussian Elimination ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Refutation Systems ◽  
Unit Propagation

AbstractState-of-the-art refutation systems for SAT are largely based on the derivation of clauses meeting some redundancy criteria, ensuring their addition to a formula does not alter its satisfiability. However, there are strong propositional reasoning techniques whose inferences are not easily expressed in such systems. This paper extends the redundancy framework beyond clauses to characterize redundancy for Boolean constraints in general. We show this characterization can be instantiated to develop efficiently checkable refutation systems using redundancy properties for Binary Decision Diagrams (BDDs). Using a form of reverse unit propagation over conjunctions of BDDs, these systems capture, for instance, Gaussian elimination reasoning over XOR constraints encoded in a formula, without the need for clausal translations or extension variables. Notably, these systems generalize those based on the strong Propagation Redundancy (PR) property, without an increase in complexity.

scholarly journals Hybrid Deduction–Refutation Systems

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 118 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Propositional Logic ◽  
Proof Theory ◽  
Natural Deduction ◽  
Basic Theory ◽  
Logical System ◽  
Classical Propositional Logic ◽  
Deductive Systems ◽  
Refutation Systems ◽  
Soundness And Completeness

Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining ‘hybrid derivation rules’ that involve both deduction and refutation. The goal of this paper is to develop a basic theory and ‘meta-proof’ theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.

scholarly journals Refutation systems for a system of nonsense-logic

2013 ◽  
Vol 20 (3) ◽  
Author(s):  
Robert Sochacki
Keyword(s):  
Refutation Systems

Refutation systems in modal logic

Studia Logica ◽  
1994 ◽  
Vol 53 (2) ◽  
pp. 299-324 ◽  
Author(s):  
Valentin Goranko
Keyword(s):  
Modal Logic ◽  
Refutation Systems
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