Connecting bilattice theory with multivalued logic

Bimodal Bilattice Logic

Bilattice Public Announcement Logic

Building on recent work on bilattice modal logic and extensions of public announcement logic to a non-classical setting, we introduce a dynamic epistemic logic having the logic of modal bilattices as propositional support. Bilattice logic is both inconsistency-tolerant and paracomplete, thus suited for applications in contexts with multiple sources of information, where one may have to deal wit...

Problems Connecting Logic and Number Theory

Bjorn Poonen discussed the “recognition problem” for finitely generated rings (and fields). That is, given two finitely generated commutative rings A and B, presented in terms of generators and relations, is there a decision procedure to determine whether or not these rings are isomorphic (this being, one would think, a basic issue for algebraic geometry!). Of course, if one drops the requireme...

Evidential Bilattice Logic and Lexical Inference

This paper presents the current state of the logic that I am using to analyse entailment, implicature and presupposition in natural language. The logic is very ne-grained and is able to make distinctions that are outside the scope of classical logic. It is independently motivated by certain properties of natural human reasoning, namely partiality , paraconsis-tency , relevance , and defeasibili...

Declarative and Operational Semantics for Bilattice-based Annotated Logic Programs

We introduce the class of normal bilattice-based annotated first-order logic programs (BAPs) and develop declarative and operational semantics for them. Thus, we discuss properties of the associated immediate consequence operators and establish their fixed-point theory. In addition, SLD-resolution for these programs is defined and its soundness and completeness established.