Related papers: Hypertableau Reasoning for Description Logics
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…
Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…
This guideline proposes a systematic and operational annotation framework for representing the structure of legal argumentation in judicial decisions. Grounded in theories of legal reasoning and argumentation, the framework aims to reveal…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
This paper considers two logics. The first one, $\mathbf{K}\mathsf{G}_\mathsf{inv}$, is an expansion of the G\"odel modal logic $\mathbf{K}\mathsf{G}$ with the involutive negation $\sim_\mathsf{i}$ defined as…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Reasoning language models, which generate long chains of thought, dramatically outperform non-reasoning language models on abstract problems. However, the internal model mechanisms that allow this superior performance remain poorly…
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory,…
We propose a multi-agent epistemic logic capturing reasoning with degrees of plausibility that agents can assign to a given statement, with $1$ interpreted as "entirely plausible for the agent" and $0$ as "completely implausible" (i.e., the…
Large Language Models (LLMs) have gained prominence in the AI landscape due to their exceptional performance. Thus, it is essential to gain a better understanding of their capabilities and limitations, among others in terms of nonmonotonic…
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…
Many high-performance models suffer from a lack of interpretability. There has been an increasing influx of work on explainable artificial intelligence (XAI) in order to disentangle what is meant and expected by XAI. Nevertheless, there is…
In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
Input/Output (I/O) logic is a general framework for reasoning about conditional norms and/or causal relations. We streamline Bochman's causal I/O logics via proof-search-oriented sequent calculi. Our calculi establish a natural syntactic…
Large Language Models (LLMs) trained on large volumes of data excel at various natural language tasks, but they cannot handle tasks requiring knowledge that has not been trained on previously. One solution is to use a retriever that fetches…
Rulelog is a knowledge representation and reasoning language based on logic programming under the well-founded semantics. It is an extension of the language of Flora-2 and so supports inheritance and other object-oriented features, as well…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD…
This paper presents a tableau calculus for finding a model for a set-satisfiable finite set of formulas of an extended fuzzy logic BL, a fuzzy logic BL with additional Baaz connective and the involutive negation, if such a model exists. The…