Any comments and suggestions are welcome!
A Canonical Class Theorem for Many Sorted Modal Logic
Abstract: In this excerpt from my master thesis I prove a variant of the Canonical Model Theorem for families of many-sorted modal logics with function symbols and mixed rigid and non-rigid constant sorts for constant domain semantics. The proof makes no assumptions about the number of sorts, safe it be countable. The logics are given axiomatically.
In fact, this is a chapter from my master thesis. It contains almost nothing but necessary definitions, lemma, propositions and proofs in order to establish the required result. But it does contain all of it in great detail…
Term-Modal Logics and Normality
Abstract: In the following paper, we investigate EA logics [i.e. Term-Modal logics] – logics for existing agents.
First, we give and introduction to modal logic and overview of current literature of EA logics. Secondly, we introduce the syntax of EA languages for n agents, semantics and an axiom system, K_{n} , for such n agents logics, which we propose as being close to what may be a minimal normal n agent EA logic. We prove soundness and completeness of this axiom system with respect to the class of all n-frames via canonical models and the proof of the Canonical Class Theorem proven for all logics extending the proposed axiom system.
I wrote this for a self-study course at Mathematics, University of Copenhagen, in 2008. The paper does contain some errors, but mainly in the form of typos — or maybe a negation where it shouldn’t be. The review of literature is far from complete as I did not know of the term ‘term-modal logic’ when I wrote the paper — see my ‘Epistemic Term-Modal Logic’ here for a better review.