In this paper, we present a new fuzzy reasoning method based on the compensating fuzzy reasoning (CFR). Its basicidea is to obtain a new fuzzy reasoning result by moving and deforming the consequent fuzzy set on the basis of themoving, deformation, and moving-deformation operations between the antecedent fuzzy set and observation information.Experimental results on real-world data sets show tha...

The present study examines the decisions made by reasoners when they are asked to revise their beliefs in the face of new, counterfactual information. Participants indicated the Scope (the degree of set inclusion) of semantic generalizations about real categories in a Pretest. In subsequent experiments, these Scope values were used to predict the willingness of participants to retain statements...

Results on approximate deduction in the context of the calculus of evidence of Dempster-Shafer and the theory of interval probabilities are reported. Approximate conditional knowledge about the truth of conditional propositions was assumed available and expressed as sets of possible values (actually numeric intervals) of conditional probabil­ ities. Under different interpretations of this condi...

Let Fm be the set of formulas formed in the usual manner by means of the infinite set {p0, p1, . . .} of propositional variables and the finite set Con of connectives. For C ∈ Con let ar(C) be the arity of C. Formulas are denoted by a, b, c, . . .. By Fm we mean the restriction of Fm into the variables po, . . . , pk−1. We assume that in terms of the connectives of Con, two peculiar (but not ne...

We introduce a new formal logic, called equality propositional logic. It has two basic connectives, $boldsymbol{wedge}$ (conjunction) and $equiv$ (equivalence). Moreover, the $Rightarrow$ (implication) connective can be derived as $ARightarrow B:=(Aboldsymbol{wedge}B)equiv A$. We formulate the equality propositional logic and demonstrate that the resulting logic has reasonable properties such a...

We present a DNA-based implementation of reaction system with molecules encoding elements of the propositional logic, that is, propositions and formulas. The protocol can perform inference steps using, for example, modus ponens and modus tollens rules and de Morgan's laws. The set of the implemented operations allows for inference of formulas using the laws of natural deduction. The system can ...

We suggest and test an integrated framework explaining how the interpretation of and the reasoning from causal conditionals (e.g., "If you fertilize a flower it will bloom") depend on exceptions. In the model availability of exceptional situations (e.g., "the flower was not watered enough") reduces the subjective conditional probability of the consequent given the antecedent, P(q p). The condit...

University students (n = 86) revised their beliefs about story-based relationships in the face of new, contradictory information. Prior to resolving an inconsistency, students drew a picture depicting the story information. Participants’ resolution of logical inconsistencies reflected (a) the structure of the facts at hand and (b) the relationship conveyed by the major premise (All p are q). St...

We hypothesized that causal conditional reasoning reflects judgment of the conditional likelihood of causes and effects based on a probabilistic causal model of the scenario being judged. Although this proposal has much in common with Cummins’ (1995) theory based on the number of disabling conditions and alternative causes, it takes more variables into account and therefore makes some differing...