This paper deals with numerical functions able to functionally express operators defined as , and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms and strong-negation functions for which it is either (Modus Ponens), or (Modus Tollens), or both, for all in and a given . Functions are taken among those in the most usual fa...

Using generalized modus ponens reasoning, we examine the values of the inferred conclusion using the Fodor’s implication in order to interpret a fuzzy if-then rule with a single input single output and the T-norms t1(x, y) = min(x, y), t2(x, y) = xy and t3(x, y) = max(0, x + y − 1) for composition operation. These are the very used T-norms in generalized modus ponens reasoning.

The main condition of the differently implicational inferencealgorithm is reconsidered from a contrary direction, which motivatesa new fuzzy inference strategy, called the double fuzzyimplications-based restriction inference algorithm. New restrictioninference principle is proposed, which improves the principle of thefull implication restriction inference algorithm. Furthermore,focusing on the ...

A novel fuzzy reasoning method, called FSI (fuzzy similarity inference) is investigated in this paper. Firstly, the unified forms of FSI which the diverse implication operators can be employed are proposed. And the computational formulas for both fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) are obtained. Secondly, the unified forms of α-FSI method are established, and the formulas for...

Using Generalized Modus Ponens reasoning, we examine the values of inferred conclusion when the premise of the rule and the observed fact have a partial overlapping. We work with fuzzy if-then rules with a single input single output and the t-norm t(x, y) = max((1+λ)(x+y−1)−λxy, 0), λ ≥ −1, for composition operation. This t-norm is important to use because for λ = −1 and λ = 0 it gives the very...

This article concerns the structure of defeasible arguments like: 'if Bob has red spots, Bob has the measles; Bob has red spots; therefore Bob has the measles.' The issue is whether such arguments have the form of modus ponens or not. Either way there is a problem. If they don't have the form of modus ponens, the common opinion to the contrary taught in leading logic textbooks is wrong. But if ...

In his [2011], Lionel Shapiro proposes a very interesting deflationist conception of logical consequence, according to which the logical-consequence predicate applying to sentences serves as a merely expressive device allowing us to talk in a generalising way about typically non-linguistic entailment facts (just as, according to a deflationist conception of truth, the truth predicate applying t...

Two nonstandard modes o f mference, conftrmatton and dental, have been shown by Bandler and Kohout to be vahd m fuzzy propositional and predicate logics. I f demal ts used m combmatton with modus ponens, the resultmg mference mode ("augmented modus ponens") ytelds more prectse bounds on the consequent of an implication than are usually called for m approximate reasoning. Slmdar results hold for...