Related papers: The modal logic of arithmetic potentialism and the…
We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
Valuation algebras abstract a large number of formalisms for automated reasoning and enable the definition of generic inference procedures. Many of these formalisms provide some notions of solutions. Typical examples are satisfying…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
G\"odel's Incompleteness Theorems suggest that no single formal system can capture the entirety of one's mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
We consider the question of extending propositional logic to a logic of plausible reasoning, and posit four requirements that any such extension should satisfy. Each is a requirement that some property of classical propositional logic be…
By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…
The existence of a (p-)optimal propositional proof system is a major open question in (proof) complexity; many people conjecture that such systems do not exist. Krajicek and Pudlak (1989) show that this question is equivalent to the…
In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…
In this paper (propositional) probability logic ($PL$) is investigated from model theoretic point of view. First of all, the ultraproduct construction is adapted for $\sigma$-additive probability models, and subsequently when this class of…
Potential theory on the complement of a subset of the real axis attracts a lot of attention both in function theory and applied sciences. The paper discusses one aspect of the theory - the logarithmic capacity of closed subsets of the real…
We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\geq\frac 12$.…
This paper introduces a new family of cognitive modal logics designed to formalize conjectural reasoning: modal systems in which cognitive contexts extend known facts with hypothetical assumptions in order to explore their consequences.…
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two…
A behavioural theory consists of machine-independent postulates characterizing a particular class of algorithms or systems, an abstract machine model that provably satisfies these postulates, and a rigorous proof that any algorithm or…
We describe a family of decidable propositional dynamic logics, where atomic modalities satisfy some extra conditions (for example, given by axioms of the logics K5, S5, or K45 for different atomic modalities). It follows from recent…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…