Related papers: Relations between assumption-based approaches in n…
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…
The reference to assumptions in how practitioners use or interact with machine learning (ML) systems is ubiquitous in HCI and responsible ML discourse. However, what remains unclear from prior works is the conceptualization of assumptions…
We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default…
Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and…
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Abstract argumentation has emerged as a method for non-monotonic reasoning that has gained popularity in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined…
Explainable AI is an emerging field providing solutions for acquiring insights into automated systems' rationale. It has been put on the AI map by suggesting ways to tackle key ethical and societal issues. Existing explanation techniques…
This paper formally compares some central notions from two well-known formalisms for rule-based argumentation, DeLP and ASPIC+. The comparisons especially focus on intuitive adequacy and inter-translatability, consistency, and closure…
We define a Kripke semantics for a conditional logic based on the propositional logic $\mathsf{N4}$, the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
In our previous research, we provided a reasoning system (called LeSAC) based on argumentation theory to provide legal support to designers during the design process. Building on this, this paper explores how to provide designers with…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
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…
We present ABA+, a new approach to handling preferences in a well known structured argumentation formalism, Assumption-Based Argumentation (ABA). In ABA+, preference information given over assumptions is incorporated directly into the…
We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…