Functional Completeness in CPL via Correspondence Analysis

Completeness via Correspondence for Extensions of the Logic of Paradox

Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (L P). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to L P by an inference scheme. Second, we define a class of natur...

Completeness and Correspondence in Chellas-Segerberg Semantics

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas-Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) nontrivial fra...

Algorithmic correspondence and completeness in modal logic

This thesis takes an algorithmic perspective on the correspondence between modal and hybrid logics on the one hand, and first-order logic on the other. The canonicity of formulae, and by implication the completeness of logics, is simultaneously treated. Modal formulae define second-order conditions on frames which, in some cases, are equivalently reducible to first-order conditions. Modal formu...

How Completeness and Correspondence Theory Got Married

It has been said that modal logic consists of three main disciplines: duality theory, completeness theory and correspondence theory; and that they are the pillars on which this edifice called modal logic rests. This seems to be true if one looks at the history of modal logic, for all three disciplines have been explicitly defined around the same time, namely in the mid-seventies. While it is ce...

Correspondence and Completeness for Generalized Quantifiers