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Synthetic Tableaux with Unrestricted Cut for First-Order Theories

Department of Logic and Cognitive Science, Faculty of Psychology and Cognitive Science, Adam Mickiewicz University, ul. Szamarzewskiego 89a, 60-568 Poznań, Poland
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Axioms 2019, 8(4), 133; https://doi.org/10.3390/axioms8040133
Received: 14 August 2019 / Revised: 13 November 2019 / Accepted: 15 November 2019 / Published: 29 November 2019
(This article belongs to the Special Issue Deductive Systems)
The method of synthetic tableaux is a cut-based tableau system with synthesizing rules introducing complex formulas. In this paper, we present the method of synthetic tableaux for Classical First-Order Logic, and we propose a strategy of extending the system to first-order theories axiomatized by universal axioms. The strategy was inspired by the works of Negri and von Plato. We illustrate the strategy with two examples: synthetic tableaux systems for identity and for partial order.
Keywords: synthetic tableaux; principle of bivalence; cut; first-order theory; universal axiom synthetic tableaux; principle of bivalence; cut; first-order theory; universal axiom
MDPI and ACS Style

Leszczyńska-Jasion, D.; Chlebowski, S. Synthetic Tableaux with Unrestricted Cut for First-Order Theories. Axioms 2019, 8, 133.

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