Lecture Notes on Completeness and Canonical Models 15-816: Modal Logic
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چکیده
In this lecture we consider a logic as the set of its tautologies. The following definition captures the closure properties that the we expect from this set of tautologies: Definition 1 (Normal modal logic) A set L of formulas is called a normal modal logic if: 1. L contains all propositional tautologies 2. (p→ q)→ ( p→ q) ∈ L for all propositional letters p, q 3. A ∈ L, (A→ B) ∈ L implies B ∈ L (closed under modus ponens) 4. A ∈ L implies A ∈ L (Gödel) 5. A ∈ L implies A′ ∈ L for all instances A′ of A (closed under instantiation). An instance results by substituting any number of propositional letters by arbitrary propositional modal formulas.
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تاریخ انتشار 2010