The size of shortest cut-free proofs of first-order formulas in intuitionistic sequent calculus is known to be non-elementary in the worst case in terms of the size of given sequent proofs with cuts of the same formulas. In contrast to that fact, we provide an elementary bound for the size of cut-free proofs for disjunction-free intuitionistic logic for the case where the cut-formulas of the or...

The aim of this paper is to test if conjunctive and disjunctive judgments are differently accounted for possibility and probability theories depending on whether (1) judgments are made on a verbal or a numerical scale, (2) the plausibility of elementary hypotheses is low or high. 72 subjects had to rate the extent to which they believe that two characters were individually, in conjunction or in...

A symmetric multiple-valued function can be realized as the disjunction of fwrdamental symmetric functions. A simpler disjunction can be formed when the latter functions combine in the same way that minterms combine to form simpler product terms for sum-of-products expressions. We solve a problem posed by Muzio [7], who seeks the worst case symmetric function in the sense that the maximum numbe...

We present CR-Prolog2, an extension of CR-Prolog with an improved semantics, and allowing ordered disjunction in the head of both regular rules and consistency-restoring rules. The new semantics yields intuitive conclusions in cases when CR-Prolog would give unintuitive results. The use of ordered disjunction often allows for a more concise, easier to read, representation of knowledge. We also ...

People make logically inconsistent probability judgments. The “Linda” problem is a well-known example, which often elicits a conjunction/disjunction fallacy: probability of constituent event A (B) judged more/less likely than their conjunction/disjunction. The Quantum Judgment model (QJM, Busemeyer et al 2011) explains such errors, which are not explainable within classical probability theory. ...

This paper is a contribution to the study of the role of disjunction in Abstract Algebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize...

Logic programs under answer set semantics have become popular as a knowledge representation formalism in Artificial Intelligence. In this paper we investigate the possibility of using answer sets for qualitative decision making. Our approach is based on an extension of the formalism, called logic programs with ordered disjunction (LPODs). These programs contain a new connective called ordered d...

This paper applies a novel automated decision-making process with TOPSIS to analyze ions and organic materials in drinking water. The hypothesis was that the modified algorithm Łukasiewicz fuzzy disjunction would be appropriate optimize water samples. maximum output values were set one apply disjunction. concentrations of samples considered from for naturally occurring chemicals health signific...

new findings of non-disjunction in autosomes of triploid females and of males carrying inversions in their autosomes seem to be desirable. It should be noted that cases of autosomal non-disjunction in males which carry inversions have already been found by Dobzhansky2 (1933) and by J. Schultz (unpublished). Dobzhansky and Darlington have observed cases of non-disjunction of autosomes cytologica...

Downward entailing linguistic environments license inferences from sets to their subsets. These environments also determine the interpretation of disjunction: Disjunction licenses a conjunctive entailment in the scope of downward entailing operators (Crain 2008, 2012). This leads to a striking asymmetry across languages in the interpretation of disjunction when it appears in the restrictor (dow...