Related papers: Grounding Rule-Based Argumentation Using Datalog
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
ASPIC-style structured argumentation frameworks provide a formal basis for reasoning in artificial intelligence by combining internal argument structure with abstract argumentation semantics. A key challenge in these frameworks is ensuring…
State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge…
We endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
Repeated executions of reasoning tasks for varying inputs are necessary in many applicative settings, such as stream reasoning. In this context, we propose an incremental grounding approach for the answer set semantics. We focus on the…
Recent years have seen increasing popularity of logic-based reasoning systems, with research and industrial interest as well as many flourishing applications in the area of Knowledge Graphs. Despite that, one can observe a substantial lack…
Warded Datalog+- extends the logic-based language Datalog with existential quantifiers in rule heads. Existential rules are needed for advanced reasoning tasks, e.g., ontological reasoning. The theoretical efficiency guarantees of Warded…
We consider interpolation from the viewpoint of fully automated theorem proving in first-order logic as a general core technique for mechanized knowledge processing. For Craig interpolation, our focus is on the two-stage approach, where…
From moderating content within an online community to producing socially-appropriate generative outputs, decision-making tasks -- conducted by either humans or AI -- often depend on subjective or socially-established criteria. To ensure…
Grounding is the task of reducing a first-order theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logic-based reasoning systems. Such systems provide a rich first-order input language…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
We describe an approach to modelling and reasoning about data-centric business processes and present a form of general model checking. Our technique extends existing approaches, which explore systems only from concrete initial states.…
This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of…
Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to…
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider…
To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. Its main focus is on formulas, as constituents of complex formalizations that are structured through formula macros, and as outputs of reasoning…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first order logic program with default negation. In a preliminary step this program…
In this paper, we offer a guide for researchers on evaluating reasoning in language models, building the case that reasoning should be assessed through evidence of adaptive, multi-step search rather than final-answer accuracy alone. Under…