Structure of Rough Approximations Based on Molecular Lattices p. 69 Rough Approximations under Level Fuzzy Sets p. 78 Fuzzy-Rough Modus Ponens and Modus Tollens as a Basis for Approximate Reasoning p. 84 Logic and Rough Sets Rough Truth, Consequence, Consistency and Belief Revision p. 95 A Note on Ziarko's Variable Precision Rough Set Model and Nonmonotonic Reasoning p. 103 Fuzzy Reasoning Base...

In this work we consider a very general principle for fuzzy rule interpolation methods based on an interpretation of the generalized modus ponens rule in terms of closeness relations. Then we present two particular instances of the general principle when the closeness relations are defined from parametric families of similarity fuzzy relations on the input and output spaces. The case of multipl...

Two important basic inference models of fuzzy reasoning are Fuzzy Modus Ponens (FMP) and Tollens (FMT). In order to solve FMP FMT problems, the full implication triple I algorithm, reverse algorithm Subsethood Inference (SIS for short) proposed, respectively. Furthermore, existing algorithms extended intuitionistic sets interval-valued according different needs. The purpose this paper is study ...

A COUNTEREXAMPLE TO MODUS PONENS* T HE rule of modus ponens, which tells us that from an indicative conditional rlf cjJ then 1/1 l, 1 together with its antecedent cjJ, one can infer 1/1, is one of the fundamental principles of logic. 2 Yet, as the following examples show, it is not strictly valid; there are occasions on which one has good grounds for believing the premises of an application of ...

This paper deals with deductive approximate reasoning techniques. Approximate reasoning is concerned with the appropriate processing of vague and uncertain knowledge, given in a rule based manner. The role model for dealing with vague and uncertain knowledge is the human mind. The ability to build abstractions and vague concepts lies at the heart of the immense capabilities of the human brain. ...

The modus ponens (A → B, A ∴ B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A → B,¬A ∴ ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antec...

We investigated whether a basic deductive inference, namely the modus ponens, is an automatic processing step carried out even in the absence of willingness to reason and awareness of all the premises. We used an exhaustive set of conditional problems concerning numbers, with a subliminal second premise, followed by a target number. Participants evaluated whether the target number was odd or ev...

[ Abstract.] The paper contains some considerations concerning the relationship between decision rules and inference rules from the rough set theory perspective. It is shown that decision rules can be interpreted as a generalization of the modus ponens inference rule, however there is an essential difference between these two concepts. Decision rules in the rough set approach are used to descri...