Unsatisfiable Formulae of Gödel Logic with Truth Constants and "Equation missing" , $$\prec $$, $$\Delta $$ Are Recursively Enumerable

Guller, Dušan

doi:10.1007/978-3-319-20469-7_27

Cited by 2 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In (Guller, 2012b;Guller, 2016a;Guller, 2014;Guller, 2015a), we have devised an extension of hyperresolution, augmented by truth constants and the equality, , strict order, ≺ ≺ ≺, projection, ∆ ∆ ∆, operators. As a side result, we have shown that unsatisfiable formulae are recursively enumerable (Guller, 2016b;Guller, 2015b).…”

Section: Introductionmentioning

confidence: 92%

Hyperresolution for Propositional Product Logic

Guller

2016

Proceedings of the 8th International Joint Conference on Computational Intelligence

Self Cite

View full text Add to dashboard Cite

We provide the foundations of automated deduction in the propositional product logic. Particularly, we generalise the hyperresolution principle to the propositional product logic. We propose translation of a formula to an equivalent satisfiable finite order clausal theory, which consists of order clauses-finite sets of order literals of the augmented form: ε 1 ε 2 where ε i is either the truth constant 0 or 1 or a conjunction of powers of propositional atoms, and is the connective or ≺. and ≺ are interpreted by the standard equality and strict order on [0, 1], respectively. We devise a hyperresolution calculus over order clausal theories, which is refutation sound and complete for the finite case. By means of the translation and calculus, we solve the deduction problem T |= φ for a finite theory T and a formula φ. Both the rules/calculi are refutation complete and sound: a clausal theory is unsatisfiable if and only 30

show abstract