Related papers: Simpler completeness proofs for modal logics with …
Standpoint logics offer unified modal logic-based formalisms for representing multiple heterogeneous viewpoints. At the same time, many non-monotonic reasoning frameworks can be naturally captured using modal logics, in particular using the…
Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only…
The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…
Focusing is a known technique for reducing the number of proofs while preserving derivability. Skolemisation is another technique designed to improve proof search, which reduces the number of back-tracking steps by representing dependencies…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
It is known that many modal and superintuitionistic logics are PSPACE-hard in languages with a small number of variables; however, questions about the complexity of similar fragments of many logics obtained by adding various axioms to…
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence,…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results…
Model checking and automated theorem proving are two pillars of formal methods. This paper investigates model checking from an automated theorem proving perspective, aiming at combining the expressiveness of automated theorem proving and…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
Epistemic logics are a primary formalism for multi-agent systems but major reasoning tasks in such epistemic logics are intractable, which impedes applications of multi-agent epistemic logics in automatic planning. Knowledge compilation…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
Dynamic logic is a modal logic for reasoning about programs. A cyclic proof system is a proof system that allows proofs containing cycles and is an alternative to a proof system containing (co-)induction. This paper introduces a sequent…
We show that the unification problem `is there a substitution instance of a given formula that is provable in a given logic?' is undecidable for basic modal logics K and K4 extended with the universal modality. It follows that the…
We define a new type of proof formalism for multi-agent modal logics with S5-type modalities. This novel formalism combines the features of hypersequents to represent S5 modalities with nested sequents to represent the T-like modality…
We define a family of propositional constructive modal logics corresponding each to a different classical modal system. The logics are defined in the style of Wijesekera's constructive modal logic, and are both proof-theoretically and…
Solovay's arithmetical completeness theorem states that the modal logic of provability coincides with the modal logic $\mathbf{GL}$. Hamkins and L\"owe studied the modal logical aspects of set theoretic multiverse and proved that the modal…
One problem to solve in the context of information fusion, decision-making, and other artificial intelligence challenges is to compute justified beliefs based on evidence. In real-life examples, this evidence may be inconsistent,…