An artificially designed Turing Machine algorithm Mo generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption P = NP , we show that Mo has a certain property, which, without the assumption, Mo does not have. This leads to P 6= NP by

In this study, electrophysiological correlates of belief-laden reasoning were investigated. As subjects, trained participants were required to draw a logical conclusion after being exposed to 4 conditional arguments: the inhibitory content of modus tollens (ICMT), facilitatory content of modus tollens (FCMT), inhibitory content of denial of the antecedent (ICDA) and facilitatory content of deni...

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...

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...

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...

Background Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given...

'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...