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Previous formulations of group theory in ACL2 and Nqthm, based on either "encapsulate" or "defn-sk", have been limited by their failure to provide a path to proof by induction on the order of a group, which is required for most interesting…
We study the logic FO(~), the extension of first-order logic with team semantics by unrestricted Boolean negation. It was recently shown axiomatizable, but otherwise has not yet received much attention in questions of computational…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs,…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
Automated fact-checking has been a challenging task for the research community. Prior work has explored various strategies, such as end-to-end training, retrieval-augmented generation, and prompt engineering, to build robust fact-checking…
This article is devoted to the study of methods to change defeasible logic programs (de.l.p.s) which are the knowledge bases used by the Defeasible Logic Programming (DeLP) interpreter. DeLP is an argumentation formalism that allows to…
We study distributed knowledge, which is what privately informed agents come to know by communicating freely with one another and sharing everything they know. Knowledge is not necessarily partitional: agents may be boundedly rational and…
We introduce infinitary action logic with exponentiation -- that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules…
In this study we explore the spontaneous apparition of visible intelligible reasoning in simple artificial networks, and we connect this experimental observation with a notion of semantic information. We start with the reproduction of a DNN…
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…
We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
The aim of this paper is to introduce the logics FFDE and FN4, which are universally free versions of Belnap-Dunn's four-valued logic, also known as the logic of first-degree entailment (FDE), and Nelson's paraconsistent logic QN4 (N-).…
W.C. Rounds and G.-Q. Zhang (2001) have proposed to study a form of disjunctive logic programming generalized to algebraic domains. This system allows reasoning with information which is hierarchically structured and forms a (suitable)…
We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding…
In this paper, the logics of the family ${\mathbb{I}}^n {\mathbb{P}}^k$:=$\{{ I^n P^k}\}_{(n,k) \in \omega^2}$ are formally defined by means of finite matrices, as a simultaneous generalization of the weakly-intuitionistic logic $I^1$ and…