Analytic Tableaux for all of SIXTEEN_3

R.A. Muskens, S. Wintein

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper we give an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t , ⊧ f , ⊧ i , and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six.
Original languageEnglish
Pages (from-to)1-15
Number of pages16
JournalJournal of philosophical logic
Early online date4 Dec 2014
DOIs
Publication statusPublished - 2014

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Tableaux
Tableau
Calculi
Entailment
Logic
Assignment

Keywords

  • Trilattice SIXTEEN 3; Tableau calculi; Functional completeness; Truth entailment; Falsity entailment; Information entailment

Cite this

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Analytic Tableaux for all of SIXTEEN_3. / Muskens, R.A.; Wintein, S.

In: Journal of philosophical logic, 2014, p. 1-15.

Research output: Contribution to journalArticleScientificpeer-review

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AB - In this paper we give an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ⊧ t , ⊧ f , ⊧ i , and ⊧ under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ⊧ relation may require six.

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