scholarly journals The RM paraconsistent refutation system

2009 ◽  
Vol 18 (1) ◽  
Author(s):  
Tomasz Skura
Keyword(s):  
Refutation System

An improved refutation system for intuitionistic predicate logic

1994 ◽  
Vol 13 (3) ◽  
pp. 361-373 ◽  
Author(s):  
Pierangelo Miglioli ◽  
Ugo Moscato ◽  
Mario Ornaghi
Keyword(s):  
Predicate Logic ◽  
Refutation System

scholarly journals Aristotle’s Syllogistic as a Deductive System

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 56 ◽  
Author(s):  
Piotr Kulicki
Keyword(s):  
Deductive System ◽  
Essential Elements ◽  
Formal Logic ◽  
Refutation System

Aristotle’s syllogistic is the first ever deductive system. After centuries, Aristotle’s ideas are still interesting for logicians who develop Aristotle’s work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz’s reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson.

scholarly journals A Syntactic Characterization of the Gabbay-de Jongh Logics

10.29007/1mcd ◽  
2018 ◽  
Author(s):  
Jeroen Goudsmit
Keyword(s):  
Propositional Logic ◽  
Sufficient Conditions ◽  
Intuitionistic Propositional Logic ◽  
Admissible Rules ◽  
Intermediate Logics ◽  
Refutation Systems ◽  
Refutation System

Skura syntactically characterised intuitionistic propositional logic among all intermediate logics by means of a Łukasiewicz-style refutation system. Another such syntactic characterisation is given by Iemhoff in terms of admissible rules. Here we offer a bridge between these results. That is to say, we provide sufficient conditions under which admissible rules yield a refutation system fully characterising the logic. In particular, we give a characterisation of the Gabbay–de Jongh logics by means of refutation systems employing ideas from admissibility.

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