Lecture Notes on Soundness and Correspondence 15-816: Modal Logic
نویسنده
چکیده
In the lecture 5 we have followed an axiomatic and a semantic approach to modal logic. But do these approaches fit together? We should not be using proof rules that make no sense semantically. Recall the axioms and proof rules we had so far Figure 1. The proof rules are sound iff they can only derive semantical consequences. Note that, unlike in the first lectures, this is an external soundness notion. We do not justify one proof rule by checking compatibility with another proof rule (internal soundness). Instead, we check compatibility of all proof rules with respect to the external mathematical objects of the semantics.
منابع مشابه
Lecture Notes on Noncorrespondence 15-816: Modal Logic
In lecture 7, we have seen how axiomatics and semantics of modal logic fit together in soundness proofs and correspondence proofs. We have seen several examples of classes of Kripke frames that are characterized by formulas of propositional modal logic. These were several special cases. But we are looking for a general correspondence result. Can we find a full correspondence result? For any for...
متن کاملLecture Notes on Completeness and Canonical Models 15-816: Modal Logic
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 ∈ ...
متن کامل