The left hand operand isĬalled the antecedent, and the right hand operand is called the consequent. This corresponds to the English if-thenĬonstruction. This is also known as "inclusive or", and corresponds to some usesĭisjunction is also infix binary, e.g., i_am_clever | Negation takesĪ single formula as its argument, e.g., ~i_am_clever, andĬonjunction is an infix binary connective, taking two formulae asĪrguments, e.g., i_am_clever & i_will_pass. The commonly used connectives of propositional logic are: To remove the if-then and other English words, connectives are used.
Lowercase alphabetic, the axiom set and conclusion become : Using the Prolog convention of starting propositions with In propositional logic, these propositions can be represented by their There are two propositions in the example: I am clever and The example is written in English, but it is easily translated into The conclusion that I am clever and I will pass is a logical The syntax of propositional logic is most easily introduced through an It is very simple to test for logical consequence in propositional logic, Propositional logic is a simple and well known language for representing These logics, and proof within these logics, are well understood and Most commonly the problems are expressed in a logic, ranging fromĬlassical propositional logic to more exotic logics, such as modal andĬurrent research in ATP is dominated by the use of classical logic, at In ATP, problems are expressed in some formal language.
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