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Propositional logic
Published in Richard E. Neapolitan, Xia Jiang, Artificial Intelligence, 2018
Richard E. Neapolitan, Xia Jiang
Example 2.29 To derive the hypothetical syllogism rule (A⇒B,B⇒C⊨A⇒C) $ (A \Rightarrow B, B \Rightarrow C{ \vDash }A \Rightarrow C) $ we first write the premises in conjunctive normal form and make each clause a premise. Our resultant premises are as follows: ¬A∨B,¬B∨C. $$ \neg A \vee B,~\neg B \vee C. $$
Neuro-Fuzzy Technology for Computerized Automation
Published in Gauri S. Mittal, Computerized Control Systems in the Food Industry, 2018
In classic logic some important inference rules used for inference are () Modusponens(A∧(A⇒B))⇒B () Modustollens(B¯∧(A⇒B))⇒A¯ () Hypotheticalsyllogism((A⇒B)∧(B⇒C))⇒(A⇒C)
Toward an information theoretic ontology of risk, resilience and sustainability and a blueprint for education - part II
Published in Sustainable and Resilient Infrastructure, 2022
Linda Nielsen, Michael Havbro Faber
The CONTAINER schema is the source domain of inferences about categories. Inferential logic, which is typically considered the epitome of conceptual reasoning in mathematics is actually spatial logic, i.e. it is embodied by virtue of our perception of objects in space as the metaphor Categories Are Containers demonstrates. CONTAINER schema inferences structure the logical concepts of ‘excluded middle’, ‘modus ponens’, ‘hypothetical syllogism’, and ‘modus tollens’, which is also the basic structure of Boolean logic, set theory, and probability theory. (see Lakoff and Nuňez, Lakoff & Núñez, 2000).