Axiomatizations for propositional and modal team logic

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented

Axiomatizations for Propositional and Modal Team Logic

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented

Axiomatizing propositional dependence logics

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, completeness and termination for each of the labeled calculi

Named Models in Coalgebraic Hybrid Logic

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding

Structural completeness in propositional logics of dependence

In this paper we prove that three of the main propositional logics of dependence (including propositional dependence logic and inquisitive logic), none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogues result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic

Team logic : axioms, expressiveness, complexity

Team semantics is an extension of classical logic where statements do not refer to single states of a system, but instead to sets of such states, called teams. This kind of semantics has applications for example in mathematical logic, verification of dynamic systems as well as in database theory. In this thesis, we focus on the propositional, modal and first-order variant of team logic. We study the classical questions of formal logic: Expressiveness (can we formalize sufficiently interesting properties of models?), axiomatizability (can all true statements be deduced in some formal system?) and complexity (can problems such as satisfiability and model checking be solved algorithmically?). Finally, we classify existing team logics and show approaches how team semantics can be defined for arbitrary other logics.Team-Semantik ist eine Erweiterung klassischer Logik, bei der Aussagen nicht über einzelne Zustände eines Systems getroffen werden, sondern über Mengen solcher Zustände, genannt Teams. Diese Art von Semantik besitzt unter anderem Anwendungen in der mathematischen Logik, in der Verifikation dynamischer Systeme sowie in der Datenbanktheorie. In dieser Arbeit liegt der Fokus auf der aussagenlogischen, der modallogischen und der prädikatenlogischen Variante der Team-Logik. Es werden die klassischen Fragestellungen formaler Logik untersucht: Ausdruckskraft (können hinreichend interessante Eigenschaften von Modellen formalisiert werden?), Axiomatisierbarkeit (lassen sich alle wahren Aussagen in einem Kalkül ableiten?) und Komplexität (können Probleme wie Erfüllbarkeit und Modellprüfung algorithmisch gelöst werden?). Schlussendlich werden existierende Team-Logiken klassifiziert und es werden Ansätze aufgezeigt, wie Team-Semantik für beliebige weitere Logiken definiert werden kann

Axiomatizing modal inclusion logic

Modal inclusion logic is modal logic extended with inclusion atoms. It is the modal variant of first-order inclusion logic, which was introduced by Galliani (2012). Inclusion logic is a main variant of dependence logic (Väänänen 2007). Dependence logic and its variants adopt team semantics, introduced by Hodges (1997). Under team semantics, a modal (inclusion) logic formula is evaluated in a set of states, called a team. The inclusion atom is a type of dependency atom, which describes that the possible values a sequence of formulas can obtain are values of another sequence of formulas. In this thesis, we introduce a sound and complete natural deduction system for modal inclusion logic, which is currently missing in the literature. The thesis consists of an introductory part, in which we recall the definitions and basic properties of modal logic and modal inclusion logic, followed by two main parts. The first part concerns the expressive power of modal inclusion logic. We review the result of Hella and Stumpf (2015) that modal inclusion logic is expressively complete: A class of Kripke models with teams is closed under unions, closed under k-bisimulation for some natural number k, and has the empty team property if and only if the class can be defined with a modal inclusion logic formula. Through the expressive completeness proof, we obtain characteristic formulas for classes with these three properties. This also provides a normal form for formulas in MIL. The proof of this result is due to Hella and Stumpf, and we suggest a simplification to the normal form by making it similar to the normal form introduced by Kontinen et al. (2014). In the second part, we introduce a sound and complete natural deduction proof system for modal inclusion logic. Our proof system builds on the proof systems defined for modal dependence logic and propositional inclusion logic by Yang (2017, 2022). We show the completeness theorem using the normal form of modal inclusion logic

Named Models in Coalgebraic Hybrid Logic

Hybrid logic extends modal logic with support for reasoning about individual states, designated by so-called nominals. We study hybrid logic in the broad context of coalgebraic semantics, where Kripke frames are replaced with coalgebras for a given functor, thus covering a wide range of reasoning principles including, e.g., probabilistic, graded, default, or coalitional operators. Specifically, we establish generic criteria for a given coalgebraic hybrid logic to admit named canonical models, with ensuing completeness proofs for pure extensions on the one hand, and for an extended hybrid language with local binding on the other. We instantiate our framework with a number of examples. Notably, we prove completeness of graded hybrid logic with local binding