formal-logic

To check argument validity using Z3, encode the premises and conclusion as satisfiability formulas, then test whether the negated conclusion is satisfiable alongside the premises. If unsatisfiable, the formal logic argument is a valid entailment.

Yes, you can solve constraint satisfaction puzzles like N-Queens and Zebra by expressing the grid variables and rules as Z3 constraints. The SMT solver performs satisfiability checks to find a valid model that satisfies all puzzle conditions.

You verify modal logic S5 validity by evaluating necessity and possibility properties under S5 Kripke frame semantics. The formal logic tool performs brute-force model checks across possible worlds to determine if the modal formula holds universally.

Z3 works alongside sympy for propositional logic reasoning by using sympy's logic utilities for symbolic manipulation and equivalence verification. This combination helps teach and verify tautologies for smaller propositional formulas before SMT encoding.

The best way to determine if a logical formula is a tautology or contradiction is translating the statement into a Z3 satisfiability check. If the negation is unsatisfiable, it is a tautology; if the original formula is unsatisfiable, it is a contradiction.

You should avoid using an SMT solver for theorem proving when working with higher-order logic systems requiring constructive proofs, or when dealing with formulas so large that brute-force satisfiability checks become computationally intractable.