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We define a class of formal systems inspired by Prawitz's theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to…
Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA…
After a few decades of development, computational argumentation has become one of the active realms in AI. This paper considers extension-based concrete and abstract semantics of argumentation. For concrete ones, based on Grossi and…
Causal inference is essential for data-driven decision-making, as it aims to uncover causal relationships from observational data. However, identifying causality remains challenging due to the potential for confounding and the distinction…
In this paper, we define an intuitionistic version of Computation Tree Logic. After explaining the semantic features of intuitionistic logic, we examine how these characteristics can be interesting for formal verification purposes.…
Substantial efforts have been made in developing various Decision Modeling formalisms, both from industry and academia. A challenging problem is that of expressing decision knowledge in the context of incomplete knowledge. In such contexts,…
The relationship between Lexical-Functional Grammar (LFG) {\em functional structures} (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that correctly explains…
The approach taken by Gheorghiu, Gu and Pym in their paper on giving a Base-extension Semantics for Intuitionistic Multiplicative Linear Logic is an interesting adaptation of the work of Sandqvist for IPL to the substructural setting. What…
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…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We take a utility-based approach to categorization. We construct generalizations about events and actions by considering losses associated with failing to distinguish among detailed distinctions in a decision model. The utility-based…
Analogical reasoning is a powerful inductive mechanism, widely used in human cognition and increasingly applied in artificial intelligence. Formal frameworks for analogical inference have been developed for Boolean domains, where inference…
An important open question in AI is what simple and natural principle enables a machine to reason logically for meaningful abstraction with grounded symbols. This paper explores a conceptually new approach to combining probabilistic…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
Recently, a novel fixed point operation has been introduced over certain non-monotonic functions between stratified complete lattices and used to give semantics to logic programs with negation and boolean context-free grammars. We prove…