Logic, Reasoning, and Knowledge

Latest papers

• ABDA-NL: A Natural-Language Scenario Explorer for Argument-Based Reasoning

  Shawn Bowers, Martin Caminada, Haoyang Liu, Bertram Lud\"ascher · 2 October 2026

  ABDA-NL adds a natural-language interface to ABDA, a system for argument-based discussion using ASPIC- knowledge bases under grounded semantics. Users see which conclusions are accepted, rejected, or undecided, open an interactive rendering of the grounded discussion game to learn why, explore what-…

• A Simple Doxastic Deontic Logic for Norm-Guided Decision Making

  Thorsten Engesser, Agata Ciabattoni · 2 October 2026

  Making decisions despite conflicting norms and incomplete or unreliable information is a fundamental challenge for autonomous systems. We introduce a simple doxastic deontic logic for this setting: a classically reducible fragment of Chellas' Minimal Deontic Logic, extended with explicit conditional…

• What Was Said, Not What Was 'Thought': Type-6 Logic for CoT Verification

  Adrian de Wynter · 1 October 2026

  We introduce Type-6 logic, a variant of dynamic epistemic logic augmented with two operators (uncertainty and recurrence), designed to model the inferential dynamics of contemporary large language model (LLM) chain-of-thought (CoT) reasoning. Type-6 accounts for common LLM reasoning pathologies such…

• Abductive World Modeling via Causal Representation Learning

  Ziqi Liu, Songhan Yang, Linfan Zhou, Jiatong Liu, Lijun Peng, Long Wan, Yinqi Bai · 30 September 2026

  The central challenge of world modeling is to learn representations that capture how the world evolves. However, existing world models predominantly represent future states without explicitly capturing the latent causes underlying their evolution, limiting their ability to reason about why and how t…

• Proofs Without Nominals: G\"odel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes

  Christoph Benzm\"uller · 30 September 2026

  The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's variants of the ontological argument (2025), reaches beyond the modal object language of the arguments: its property quantifiers range over terms that ma…

• Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

  Till Hofmann, Stefan Schupp, Gerhard Lakemeyer · 23 September 2026

  Representing time is crucial for cyber-physical systems and has been studied extensively in the situation calculus. The most commonly used approach represents time by adding a real-valued function $\mathit{time}(a)$ that attaches a time point to each action and consequently to each situation. We sho…

• Stable Marriage Problems with Ties and Incomplete Preferences: An Empirical Comparison of ASP, SAT, ILP, CP, and Local Search Methods

  Selin Eyupoglu, Muge Fidan, Yavuz Gulesen, Ilayda Begum Izci, Berkan Teber, Baturay Yilmaz, Ahmet Alkan, Esra Erdem · 23 September 2026

  We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and Incomplete preferences (SMTI). We consider three optimization …

• PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations

  Julian Eggert (Honda Research Institute Europe, Offenbach, Germany) · 18 September 2026

  Allen's interval algebra is a qualitative calculus for temporal relations, but its thirteen base relations are crisp predicates over exact interval boundaries. This is inadequate for temporal information from language, perception, databases, or uncertain histories, where times, durations, and bounda…

• Semantic Knowledge Technologies: what the Semantic Web lost sight of, and what it never had

  Achille Zappa · 15 September 2026

  The Semantic Web set out to give information a machine-interpretable form so that software could integrate and reason over it. Its standards became scientific knowledge infrastructure, but the machine competence it promised did not follow, and the systems now answering questions over scientific know…

• The Semantic Elevation Operator and the Closure of the Undecidable Class under Preservation

  Jose Pascual Gumbau Mezquita · 11 September 2026

  The undecidability of a program's static semantic properties is governed by Rice's theorem. Self-modifying systems, however, require analysing not whether a property holds now, but whether it is preserved when the system rewrites itself. We formalise this transition through a semantic elevation oper…

• Monadic Second-Order Logic in HOL: Deep and Shallow with Automated Faithfulness (Extended Preprint)

  Christoph Benzmueller, Daniel Kirchner · 9 September 2026

  In Isabelle/HOL, we apply the deep-and-shallow embedding methodology of our prior work to monadic second-order logic (MSO). Three embeddings are developed side by side: a deep embedding (an inductive datatype with an explicit satisfaction relation); a maximal-shallow embedding that translates the co…

• Three Types of Negation of Triple and its Elements and an Extension of Triple

  Zhenghua Pan · 9 September 2026

  In various data models, the classical triple is a typical semantic data model. However, due to the design of the triple as a simple structure for representing positive assertions, it cannot sufficiently express different forms of negation present in the triple and its elements. This paper conceptual…

• Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation

  Zhenghua Pan · 9 September 2026

  Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfactual reasoning is a process of reasoning based on counterfactuals. Negation is an indispensable core concept in them. In this paper, based on the logi…

• Relative Prime Factorization and Finite-State Presentations under Fixed Finite-Monoid Observation

  Takayuki Kuriyama · 4 September 2026

  Let $L\subseteq\Sigma^*$ and fix a morphism $h:\Sigma^*\to M$ into a finite monoid. We study exact factorization and canonical presentation in the relative syntactic congruence $\theta_{L,h}:=\equiv_L\cap\ker h$. We separate unique factorization from finite direct presentation. An exhaustively com…

• Causal-Counterfactual RAG: The Integration of Causal-Counterfactual Reasoning into RAG

  Harshad Khadilkar, Abhay Gupta · 4 September 2026

  Large language models (LLMs) have transformed natural language processing (NLP), enabling diverse applications by integrating large-scale pre-trained knowledge. However, their static knowledge limits dynamic reasoning over external information, especially in knowledge-intensive domains. Retrieval-Au…

• Evidential-Based Higher-Order Set Argumentation Framework

  Shuai Tang · 31 August 2026

  Evidential argumentation extends Dung's abstract argumentation by requiring arguments and interactions to be backed by chains of evidence rooted in prima-facie elements. However, existing formalisms lack a unified treatment of evidential support, higher-order relations (attacks and supports targetin…

• Context Localization for Generalized Level-Based Evaluation in Knowledge-Based Systems

  Ondrej Hutn\'{i}k, Nat\'{a}lia Pu\v{s}k\'{a}rov\'{a} · 31 August 2026

  We study context localization for generalized level-based evaluation in knowledge-based systems. The framework models situations where a structured nonnegative score, defined on facts, rules, cases, criteria or evidence units, is evaluated through conditional aggregation tests on admissible knowledg…

• Compositional Generalization via Structural Identification in a Category-Theoretic Framework

  Akihiro Maeda, Thomas Seiller, Yohei Oseki · 28 August 2026

  Compositional generalization is usually evaluated through model accuracy. We instead ask which structural or lexical identifications make held-out COGS examples admissible from the structures observed in training. Sentences are represented as functors from syntactic addresses to lexical tokens, and …

• The Imperfective Paradox Is Not Necessarily in Large Language Models: A Benchmark Failure Before a Model Failure

  Kaiqiao Han, Yizhou Sun · 27 August 2026

  The imperfective paradox provides a useful test of compositional semantic analysis. Recent work constructs an NLI benchmark and reports that models frequently infer completed telic events from progressive descriptions, attributing this behavior to a Teleological Bias. It further argues that promptin…

• A Mathematical Theory of Interpretation: Rational Entropy, Spectral Readout, and Confusability as a Resource

  Blake Reynolds · 26 August 2026

  This article presents the abridged core of \emph{A Mathematical Theory of Interpretation} (MTI), which treats interpretation as observer-relative spectral measurement under an access structure. MTI makes interpretation a method-design problem: access, query, utility, and medium determine what an obs…

• Distinguishing Revision and Delayed Elaboration in Incremental Narrative Interpretation

  Yi-Chun Chen · 25 August 2026

  Both human and AI systems that process narrative or long-form content operate incrementally: input is received over time, and internal representations must be updated accordingly. Incremental interpretation, therefore, depends not only on what is represented but also on how the representational stat…

• Identifying Implicit Premises for Logical Reconstruction of Argument Graphs

  Xuyao Feng, Anthony Hunter · 20 August 2026

  The logical reconstruction of argument graphs from natural language text is challenging because of the prevalence of enthymemes (i.e., arguments with implicit premises). There are natural language processing methods for identifying enthymemes in text, and there are symbolic methods based on abductio…

• Formal Verification of Romanov's Triplet Logic: A Verified Filter for Sliding-window 3-CNF with Application to Structured Formulas

  Dmitry V. Alexandrov · 20 August 2026

  We present the first mechanised formalisation of Romanov's Triplet Logic (TLS) in the Rocq proof assistant. TLS is a triplet-based combinatorial framework for reasoning about compatible paths through layered triplet structures, called Compact Triplets Structures (CTS), and their intersection via Rom…

• Syntactic Simplification of OWL Class Expressions

  Alkid Baci, N'Dah Jean Kouagou, Caglar Demir, Axel-Cyrille Ngonga Ngomo · 20 August 2026

  Class expression learning often produces complex OWL class expressions that are difficult to interpret and reason over. However, by following theoretically grounded simplification principles, this complexity can be reduced. In this paper, we propose Class Expression Simplifier (CES), a novel algorit…

• Pairwise Logical Selection of Enthymeme Completions under Semantic-Link Uncertainty

  Xuyao Feng, Antonis Bikakis · 20 August 2026

  Arguments often omit premises or claims, forming enthymemes. We study pairwise logical selection between two candidates for the omitted component. Existing natural language methods can identify or generate candidates but often do not expose how the selected candidate completes the inference, while l…