Related papers: Non-Monotonic S4F Standpoint Logic (Extended Versi…
A modal logic based on quantum logic is formalized in its simplest possible form. Specifically, a relational semantics and a sequent calculus are provided, and the soundness and the completeness theorems connecting both notions are…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
This paper develops a new approach to computational argumentation that is informed by philosophical and linguistic views. Namely, it takes into account two ideas that have received little attention in the literature on computational…
The syntactic nature of logic and computation separates them from other fields of mathematics. Nevertheless, syntax has been the only way to adequately capture the dynamics of proofs and programs such as cut-elimination, and the finiteness…
We propose a "modal linear logic" to reformulate intuitionistic modal logic S4 (IS4) in terms of linear logic, establishing an S4-version of Girard translation from IS4 to it. While the Girard translation from intuitionistic logic to linear…
Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Gradual semantics (GS) have demonstrated great potential in argumentation, in particular for deploying quantitative bipolar argumentation frameworks (QBAFs) in a number of real-world settings, from judgmental forecasting to explainable AI.…
The logics $\mathsf{CS4}$ and $\mathsf{IS4}$ are the two leading intuitionistic variants of the modal logic $\mathsf{S4}$. Whether the finite model property holds for each of these logics have been long-standing open problems. It was…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
We observe some puzzling linguistic data concerning ordinary knowledge ascriptions that embed an epistemic (im)possibility claim. We conclude that it is untenable to jointly endorse both classical logic and a pair of intuitively attractive…
To resolve conflicts among norms, various nonmonotonic formalisms can be used to perform prioritized normative reasoning. Meanwhile, formal argumentation provides a way to represent nonmonotonic logics. In this paper, we propose a…
We revisit the issue of connections between two leading formalisms in nonmonotonic reasoning: autoepistemic logic and default logic. For each logic we develop a comprehensive semantic framework based on the notion of a belief pair. The set…
We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Unlike previous approaches to belief change in logic programming, our formal techniques are analogous to those of distance-based belief…
Dealing with uncertain, contradicting, and ambiguous information is still a central issue in Artificial Intelligence (AI). As a result, many formalisms have been proposed or adapted so as to consider non-monotonicity, with only a limited…
This paper studies the modal logical aspects of provability predicates and consistency statements for theories of arithmetic. First, we provide an overview of previous works on the correspondence between various derivability conditions for…
Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…