Related papers: A basic system of paraconsistent Nelsonian logic o…

We present a logic for the reasoning about necessity and justifications which is independent from relational semantics. We choose the concept of justification -- coming from a class of "Justification Logics" (Artemov 2008, Fitting 2009) --…

Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based…

We present a novel formalization of counterfactual conditionals in a quantified modal logic. Counterfactual conditionals play a vital role in ethical and moral reasoning. Prior work has shown that moral reasoning systems (and more…

In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…

Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…

Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…

Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

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…

We show that first-order logic can be translated into a very simple and weak logic, and thus set theory can be formalized in this weak logic. This weak logical system is equivalent to the equational theory of Boolean algebras with three…

The famous van Benthem theorem states that modal logic corresponds exactly to the fragment of first-order logic that is invariant under bisimulation. In this article we prove an exact analogue of this theorem in the framework of modal…

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…

Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…

We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification…

We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another…

Bayesian reasoning plays a significant role both in human rationality and in machine learning. In this paper, we introduce transfinite modal logic, which combines modal logic with ordinal arithmetic, in order to formalize Bayesian reasoning…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

The different semantics that can be assigned to a logic program correspond to different assumptions made concerning the atoms whose logical values cannot be inferred from the rules. Thus, the well founded semantics corresponds to the…

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…

We consider the G\"odel bi-modal logic determined by fuzzy Kripke models where both the propositions and the accessibility relation are infinitely valued over the standard G\"odel algebra [0,1] and prove strong completeness of Fischer Servi…