In order to get a more general result related on fuzzy implications that induced by aggregation functions, we relax the definition of overlap precisely, removing its right-continuous, and introduce new kind function, which called semi-overlap function. Subsequently, explore some their algebraic properties corresponding residual implications. Moreover, serval scholars have provided kinds methods...

Modus ponens provides the central theme. There are laws, of the form A → C. A logic (or other theory) L collects such laws. Any datum A (or theory T incorporating such data) provides input to the laws of L. The central ternary relation R relates theories L; T and U , where U consists of all of the outputs C got by applying modus ponens to major premises from L and minor premises from T . Underl...

Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsis-tent, or non-trivializable, logic is, by necessity, a compromise, or weakening , of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in ...

Monotonic relationship between input and output often is an inherent property of fuzzy systems. For example, for a cart-pole system, there is a gradual relationship between the pole angle and the cart velocity of the form: “The more the pole deviates from the upright position, the higher velocity the cart must gain”. Thus, we propose an approach, that we call Gradual GMP, which is able to integ...

In this paper, based on the our previous researchs about generalized modus ponens with linguistic modifiers for If ... Then rules, we propose generalized If...Then...Else inference rules with linguistic modifiers in linguistic many–valued logic framework with using hedge moving rules for approximate reasoning.

Rule based fuzzy approximate reasoning uses various techniques of modified modus ponens. The observation is in most cases not identical with any of the antecedents in the rules. However, a conclusion still can be computed by using some combination of all consequents where an overlapping of observation and antecedent is present. If the rule base is sparse, i.e., it contains insufficient informat...

Human conditional reasoning is defeasible: people withdraw logically valid conclusions if they are aware of situations (i.e., exceptions) that prevent the consequent of the rule to happen although the antecedent is given. In this paper we investigate defeasible reasoning with quantified rules. In two experiments we rephrased conditionals from the literature (Experiment 1) and rules from penal c...

'Aristotelian logic', as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as 'hypothetical syllogisms'. However, Aristotle did not discuss such arguments, no...

Rationality requires various things of you. For example, it requires you not to have contradictory beliefs, and to intend what you believe is a necessary means to an end that you intend. Suppose rationality requires you to F. Does this fact constitute a reason for you to F? Does it even follow from this fact that you have a reason to F? I examine these questions and reach a sceptical conclusion...