Related papers: {\L}-Axiomatizability in intermediate and normal m…
We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal…
The unification problem in a propositional logic is to determine, given a formula F, whether there exists a substitution s such that s(F) is in that logic. In that case, s is a unifier of F. When a unifiable formula has minimal complete…
We prove expressive completeness results for convex propositional and modal team logics, where a logic is convex if, for each formula, if it is true in two teams $t$ and $u$ and $t\subseteq s\subseteq u$, then it is also true in $s$. We…
In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
We provide a characterization of those relation algebras which are isomorphic to the algebras of compatible relations of some $\Z_2$-set. We further prove that this class is finitely axiomatizable in first-order logic in the language of…
We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…
We consider a family of two-valued "fully evaluated left-sequential logics" (FELs), of which Free FEL (defined by Staudt in 2012) is most distinguishing (weakest) and immune to atomic side effects. Next is Memorising FEL, in which…
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We develop the first two heap logics that have implicit heaplets and that admit FO-complete program verification. The notion of FO-completeness is a theoretical guarantee that all theorems that are valid when recursive definitions are…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
In this paper we study the interaction between logic and probability. In particular, we show that the convex hull of evaluations of a broad class of logics is always effectively axiomatizable. We define a Birkhoff-style calculus for…
We generalize the theory of stable canonical rules by adopting definable filtration, a generalization of the method of filtration. We show that for a modal rule system or a modal logic that admits definable filtration, each extension is…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…
We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…
This thesis aims to provide a suite of techniques to generate completeness results for coalgebraic logics with axioms of arbitrary rank. We have chosen to investigate the possibility to generalize what is arguably one of the most successful…
We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal logic it is also a logic of terms that admits a (sound)…
We show that if A is a linear order then Th(A) is either $\aleph_0$-categorical or Borel complete (in the sense of Friedman and Stanley). We generalize this; if A has countably many unary predicates attached, then Th(A) is…