On Finite Logics

Extending states on finite concrete logics

In this note we collect several observations on state extensions. They may be instrumental to anyone who pursues the theory of quantum logics. In particular, we find out when extensions (resp. signed extensions) exist in the “concrete” concrete logic of all even-element subsets of an evenelement set (Th 2.3 and Th 2.9). We also mildly add to the study of difference-closed logics as initiated in...

Completeness for Logics on Finite Traces

Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. We propose that existing methods for proving deductive completeness for infinite-trace logics are effective on their finite counterparts. To adapt proofs for infinite-trace logics, we “inject” finiteness: that is, we alter the proof structure to ensure that models are finite. As evidence for...

Finite variable logics

In this survey article we discuss some aspects of finite variable logics. We translate some well-known fixed-point logics into the infinitary logic L∞ω, discussing complexity issues. We give a game characterisation of L∞ω, and use it to derive results on Scott sentences. In this connection we consider definable linear orderings of types realised in finite structures. We then show that the Craig...

On the Expressive Power of Logics on Finite Models

Logics of Finite Hankel Rank

We discuss the Feferman-Vaught Theorem in the setting of abstract model theory for finite structures. We look at sum-like and product-like binary operations on finite structures and their Hankel matrices. We show the connection between Hankel matrices and the FefermanVaught Theorem. The largest logic known to satisfy a Feferman-Vaught Theorem for product-like operations is CFOL, first order log...