scholarly journals Automated Proof Search System for Logic of Correlated Knowledge

Author(s):  
Haroldas Giedra ◽  
Romas Alonderis
Author(s):  
Neil Tennant

Parallelized elimination rules in natural deduction correspond to Left rules in the sequent calculus; and introduction rules correspond to Right rules. These rules may be construed as inductive clauses in the inductive definition of the notion of sequent proof. There is a natural isomorphism between natural deductions in Core Logic and the sequent proofs that correspond to them. We examine the relations, between sequents, of concentration and dilution; and describe what it is for one sequent to strengthen another. We examine some possible global restrictions on proof-formation, designed to prevent proofs from proving dilutions of sequents already proved by a subproof. We establish the important result that the sequent rules of Core Logic maintain concentration, and we explain its importance for automated proof-search.


2020 ◽  
Vol 28 (3) ◽  
pp. 413-413
Author(s):  
R Alonderis ◽  
H Giedra
Keyword(s):  

Author(s):  
Wilfried Sieg ◽  
Farzaneh Derakhshan
Keyword(s):  

2019 ◽  
Vol 28 (3) ◽  
pp. 261-280 ◽  
Author(s):  
R Alonderis ◽  
H Giedra

Abstract The cut-free Gentzen-type sequent calculus LLK for the logic of likelihood (LL) is introduced in the paper. It is proved that the calculus is sound and complete for LL. Using the introduced calculus LLK, a decision procedure for LL is presented.


2014 ◽  
Vol 20 ◽  
pp. 222-245
Author(s):  
А. Е. Болотов ◽  
В. О. Шангин

In this paper we present the automated proof search technique in natural deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p _ ¬p, are not valid. In this paper we formulate the natural deduction system for paracomplete logic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs.


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