Related papers: Analytic Tableaux for Justification Logics
Justification logic is a term used to identify a relatively new family of modal-like logics. There is an established literature about propositional justification logic, but incursions on the first-order case are scarce. In this paper we…
We discuss tableaux for the Implicational Propositional Calculus and show how they may be used to establish its completeness.
A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However,…
We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…
In this paper we present two terminating tableau calculi for propositional Dummett logic obeying the subformula property. The ideas of our calculi rely on the linearly ordered Kripke semantics of Dummett logic. The first calculus works on…
This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Different theorem provers tend to produce proof objects in different formats and this is especially the case for modal logics, where several deductive formalisms (and provers based on them) have been presented. This work falls within the…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
This paper considers two logics. The first one, $\mathbf{K}\mathsf{G}_\mathsf{inv}$, is an expansion of the G\"odel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim_\mathsf{i}$ defined as…
The present paper provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. Dynamic epistemic logic is one of the best known members of a family of logical systems which…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
Artificial Intelligence (AI) is being increasingly used to develop systems that produce intelligent solutions. However, there is a major concern that whether the systems built will be trusted by humans. In order to establish trust in AI…
Explainable AI (XAI) in high-stakes domains should help stakeholders trust and verify system outputs. Yet Chain-of-Thought methods reason before concluding, and logical gaps or hallucinations can yield conclusions that do not reliably align…
Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…