Modus ponens (from A and “if A then C” infer C; short: MP) is one of the most basic inference rules. The probabilistic MP allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P (A) and P (C|A) infer P (C)). In this paper, we generalize the probabilistic MP by replacing A by the conditional event A|H . The resulting inference rule...

Based on our previous researchs about generalized modus ponens (GMP) with linguistic modifiers for If ... Then rules, this paper proposes new generalized modus tollens (GMT) inference rules with linguistic modifiers in linguistic many–valued logic framework with using hedge moving rules for inverse approximate reasoning.

Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed by Zadeh [1] in our ...

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B (e.g., from If it rained, Alicia got wet and It rained to Alicia got wet). Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise (e.g., If she forgot her umbrella, Alicia got wet) can lower partic...

Holographic reduced representation is based on a suitable distributive coding of structured information in conceptual vectors, which elements satisfy normal distribution N(0,1/n). Existing applications of this approach concern various models of associative memory that exploit a simple algebraic operation of scalar product of distributed representations to measure an overlap between two structur...

Byrne (1989) claims to have demonstrated that context can suppress valid inferences like modus ponens. If substantiated, the claim would refute the idea that valid inferences cannot be countermanded without contradiction, although implicatures and invited inferences can be (e.g., Braine & Rumain, 1981; Geis & Zwicky, 1971; Grice, 1975). That, in turn, would invalidate one of the few available m...

Combinatory logic is based on modus ponens and a schematic (polymorphic) interpretation of axioms. In this paper we propose to consider expressive combinatory logics under the restriction that axioms are not interpreted schematically but ,,literally”, corresponding to a monomorphic interpretation of types. We thereby arrive at finite combinatory logic, which is strictly finitely axiomatisable a...