Entailment defines the logical connection where true premises guarantee a true conclusion. It's fundamental to deductive reasoning, ensuring that if…
An elimination rule in logic simplifies formulas by removing connectives or quantifiers. It's crucial for deriving conclusions from premises, forming…
A technique in mathematical logic to remove quantifiers from formulas, preserving logical equivalence. Crucial in theories like real closed fields…
Elementary equivalence signifies that two structures share all the same first-order sentences. This concept is crucial in model theory for…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
Dynamic modal logic explores necessary and possible connections between events. It extends traditional modal logic to analyze how states change…
The dual of a truth-table involves swapping truth values. Connectives like conjunction and disjunction are dual. The dual of a…
Doxastic modal logic explores the reasoning behind beliefs. It models how rational agents form and update their beliefs, providing a…
The double turnstile (⊨) symbol signifies semantic entailment or logical consequence. It indicates that the truth of certain propositions guarantees…
The principle of double negation introduction states that for any proposition P, P implies the double negation of P (¬¬P).…