Topic
Modus ponens
About: Modus ponens is a research topic. Over the lifetime, 819 publications have been published within this topic receiving 15745 citations. The topic is also known as: modus ponendo ponens & MP.
Papers published on a yearly basis
Papers
More filters
TL;DR: F fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc.
Abstract: The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, ℐ, of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in ℐ as a fuzzy subset of [0, 1]. Since ℐ is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in ℐ requires, in general, a linguistic approximation by a truth-value in ℐ. As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. Approximate reasoning is viewed as a process of approximate solution of a system of relational assignment equations. This process is formulated as a compositional rule of inference which subsumes modus ponens as a special case. A characteristic feature of approximate reasoning is the fuzziness and nonuniqueness of consequents of fuzzy premisses. Simple examples of approximate reasoning are: (a) Most men are vain; Socrates is a man; therefore, it is very likely that Socrates is vain. (b) x is small; x and y are approximately equal; therefore y is more or less small, where italicized words are labels of fuzzy sets.
1,273 citations
TL;DR: This paper deals with the properties of their methods in the case of 'generalized modus tollens', and investigates the other new fuzzy reasoning methods obtained by introducing the implication rules of many valued logic systems.
493 citations
TL;DR: This paper provides axioms for a simple problem in temporal reasoning which has long been identified as a case of default reasoning, thus presumably amenable to representation in nonmonotonic logic, and finds that the logics considered are inherently incapable of representing this kind ofdefault reasoning.
484 citations
TL;DR: Three experiments are reported which show that in certain contexts subjects reject instances of the valid modus ponens and modus tollens inference form in conditional arguments and suggest that the interpretation of premises plays an even more central role in reasoning than has previously been admitted.
447 citations
TL;DR: Investigation of the relative contributions of syntactic form and content to conditional reasoning found conclusions of arguments based on conditionals with few alternative causes or disabling conditions were found to be more accept-able than conclusions based on those with many.
Abstract: An experiment was conducted to investigate the relative contributions of syntactic form and content to conditional reasoning The content domain chosen was that of causation Conditional statements that described causal relationships (if 〈cause〉, then (〈effect〉) were embedded in simple arguments whose entailments are governed by the rules -of truth-functional logic (ie,modus ponens, modus tollens, denying the antecedent, andaffirming the consequent) The causal statements differed in terms of the number of alternative causes and disabling conditions that characterized the causal relationship (A disabling condition is an event that prevents an effect from occurring even though a relevant cause is present) Subjects were required to judge whether or not each argument’s conclusion could be accepted Judgments were found to vary systematically with the number of alternative causes and disabling conditions Conclusions of arguments based on conditionals with few alternative causes or disabling conditions were found to be more accept-able than conclusions based on those with many
314 citations