The relation between partial deduction and the unfold/fold approach has been a matter of intense discussion. In this paper we consolidate the advantages of the two approaches and provide an extended partial deduction framework in which most of the tupling and deforestation transformations of the fold/unfold approach, as well the current partial deduction transformations, can be achieved. Moreov...

We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositio...

Abstract The paper introduces a new type of rules into Natural Deduction, elimination by composition. Elimination composition replace usual in the style disjunction and give more direct treatment additive disjunction, multiplicative conjunction, existence quantifier possibility modality. have an enormous impact on proof-structures deductions: they do not produce segments, deduction trees remain...

Mathematical deduction is not useful to the physicist if interpreted rigorously. It is necessary to know that its validity is unaltered when the premise and conclusion are only ”approximately true”. But the indeterminacy thus introduced, it is necessary to add in criticism, well invalidate the deduction unless the permissible limits of variation are specified. The same need was expressed by L.A...

This paper proves strong normalization of classical natural deduction with disjunction and permutative conversions, by using CPS-translation and augmentations. By them, this paper also proves strong normalization of classical natural deduction with general elimination rules for implication and conjunction, and their permutative conversions. This paper also proves natural deduction can be embedd...

In other words, abduction, deduction, and induction work together to explore. In recent years many Monte Carlo simulations have been.induction and abduction reasoning operators, resulting in the proposal that our. Deduction, generalized induction and generalized abduction. Have been implemented and tested within a simulation environment 5.Deduction, Quantitative and Qualitative Induction, Abduc...

CHIAKI SAKAMA AND HIROHISA SEKI y. This paper presents a partial deduction method in disjunctive logic programming. Partial deduction in normal logic programs is based on unfolding between normal clauses, hence it is not applicable to disjunctive logic programs in general. Then we introduce a new partial deduction technique, called disjunctive partial deduction, which preserves the minimal mode...