Complexity thresholds in inclusion logic

Inclusion logic differs from many other logics of dependence and independence in that it can only describe polynomial-time properties. In this article we examine more closely connections between syntactic fragments of inclusion logic and different complexity classes. Our focus is on two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. We also present a safety game for the maximal subteam membership problem and use it to investigate this problem over teams in which one variable is a key. Furthermore, we relate our findings to consistent query answering over inclusion dependencies, and present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models. (C) 2021 The Author(s). Published by Elsevier Inc.Peer reviewe

Robinson consistency in many-sorted hybrid first-order logics

In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem

Tractability Frontier of Data Complexity in Team Semantics

Peer reviewe

Subset Semantics for Justifications

Justification logic is a variant of modal logic where the modal operators are replaced be justification terms. So we deal with formulas like t:A where t is a term denoting some justification that justifies the formula A. There are many justification logics among which the Logic of Proof established by Artemov was the first. However, since a long time the framework of justification logic is also used in a wide range of epistemic logics. In this field justification terms represent reasons to belief or know something. A standard interpretation of a justification term t is then the set of formulas that are supported by the reason t. This thesis establishes in the first part another way to interpret terms, namely as sets of worlds. We use so-called subset models in which t:A is true in a normal world, when the interpretation of t in this world is a subset of the truthset of A. These models are shown to be sound and complete towards a whole family of justification logics, including the Logic of Proof. As is shown in the second part of this thesis, subset models can easily be adapted to model new kinds of justification terms and operations: finer distinctions between several variants of combining justifications, justifications with presumptions, probabilistic evidence. Furthermore, it is shown, how subset models can be used to model dynamic reasoning and forgetting