Let's say I have a set of three logical statements:
- If it is sunny AND it is the weekend then I play football (S * W -> F)
- If it is NOT sunny OR it is NOT the weekend then I do NOT play football (!S + !W -> !F)
- If it is NOT sunny AND it is NOT the weekend then I play football (!S * !W -> F)
I can show that the antecedents are complete, i.e. at least one antecedent is true for all combinations in a truth table. I can show that there is at least one combination that is not unique, i.e. more than one antecedent is true for the same combination in a truth table.
You may notice that in the case of Statement 2 the consequent is 'I do NOT play football when S=0 and W=0' which conflicts with the consequent of Statement 3 which is I do play football.
Whilst grounded in predicate or propositional logic is it possible to test whether the consequent of a set of logical statements are conflicting with one another or not?