Open AccessMultisequent Gentzen Deduction Systems For B<sub>2</sub> <sup>2</sup>-Valued First-Order Logic
Author(s) -
Wei Li,
Yuefei Sui
Publication year - 2018
Publication title -
artificial intelligence research
Language(s) - English
Resource type - Journals
eISSN - 1927-6982
pISSN - 1927-6974
DOI - 10.5430/air.v7n1p53
Subject(s) - soundness , sequent , sequent calculus , mathematics , generalization , order (exchange) , completeness (order theory) , discrete mathematics , calculus (dental) , computer science , programming language , mathematical analysis , mathematical proof , economics , dentistry , finance , medicine , geometry
For the four-element Boolean algebra B 2 2 , a multisequent Г|Δ| ∑|∏ is a generalization of sequent Г →Δ in traditional B 2 2 valued first-order logic. By defining the truth-values of quantified formulas, a Gentzen deduction system G 2 2 for B 2 2 -valued first-order logic will be built and its soundness and completeness theorems will be proved.
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