Rule of inference

Rule of inference

A rule of inference is a method or principle used in propositional calculus to arrive at a valid conclusion based on certain statements, assumed to be true, which are called hypotheses. The only rule of inference is modus ponens, which allows for the deduction of a conclusion from two premises, one of which affirms the antecedent of a conditional statement and the other affirms the consequent.From: CRC Standard Mathematical Tables and Formulae [2019], Generalisation of proof simulation procedures for Frege systems by M.L. Bonet and S.R. Buss [2018]

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Published in Dan Zwillinger, CRC Standard Mathematical Tables and Formulas, 2018

Dan Zwillinger

A rule of inference in propositional calculus is a method of arriving at a valid (true) conclusion, given certain statements, assumed to be true, which are called the hypotheses. For example, suppose that P and Q are compound statements. Then if P and P → Q are true, then Q must necessarily be true. This follows from the modus ponens tautology in the above list of tautologies. We write this rule of inference

Knowledge Representation and Processing

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Published in Clarence W. de Silva, Intelligent Control, 2018

Clarence W. de Silva

Rules of inference are used in reasoning associated with knowledge processing in order to make inferences. Two rules of inference are discussed here: Conjunction rule of inference (CRI)Modus ponens rule of inference (MPRI)

Reasoning about manipulation in multi-agent systems

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Published in Journal of Applied Non-Classical Logics, 2022

Christopher Leturc, Grégory Bonnet

Given the constraints on our frame, the associated axiomatic system is given in Figure 4. Here means that φ is a theorem. For all modalities , we have the modus ponens (MP), the substitution (SUB) and the rule of inference (RE), i.e. from , we infer . However, the rule of necessitation (NEC) is only verified for normal modalities, i.e. for all , from , we infer . Finally, we have duality (DUAL), i.e. for all , .

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Knowledge Representation and Processing

Reasoning about manipulation in multi-agent systems