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#formal-logic News & Analysis

15 articles tagged with #formal-logic. AI-curated summaries with sentiment analysis and key takeaways from 50+ sources.

15 articles
AIBullisharXiv – CS AI · Jun 97/10
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Sound and Complete Neurosymbolic Reasoning with LLM-Grounded Interpretations

Researchers present a neurosymbolic reasoning method that integrates large language models into formal logic systems using paraconsistent logic, enabling sound and complete reasoning while leveraging LLM knowledge. The approach improves factuality evaluation by 6 percentage points and successfully identifies logical contradictions in medical knowledge bases without causing logical explosion.

AINeutralarXiv – CS AI · Jun 235/10
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From numerical proportions to analogical proportions between probabilities

This academic paper extends analogical proportion theory from numerical and vector-based representations to probabilistic settings, investigating whether probability distributions associated with analogically proportional profiles maintain proportional relationships. The research bridges formal logic with statistical inference, potentially enabling more sophisticated classification methods that operate on probabilistic data.

AINeutralarXiv – CS AI · Jun 235/10
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Some Results about the Expressivity of Preference-Incomplete Structured Argumentation Frameworks

This academic paper investigates the expressive power of ASPIC+ argumentation frameworks when preference information is incomplete, comparing them against abstract formalisms with uncertain defeats. The research yields mostly negative results regarding expressivity limitations, while proposing a conjecture about a potential threshold for uncertain preference frameworks.

AINeutralarXiv – CS AI · Jun 236/10
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Understanding Privacy by Formalizing It

Researchers propose using multi-modal logic to formally define privacy as an epistemic right within normative position theory, addressing the need for rigorous algorithmic specifications of privacy protections in AI and technology development. This formalization effort aims to bridge the gap between societal consensus on privacy rights and their practical implementation in technological systems.

AINeutralarXiv – CS AI · Jun 196/10
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QMFOL: Benchmarking Large Language Model Reasoning via Quantifiable Monadic First-Order Logic Test Case Generation

Researchers introduce QMFOL, an automated framework for generating controlled-complexity logical reasoning benchmarks to evaluate large language models. The resulting QMFOLBench dataset of 2,880 instances reveals that LLM reasoning performance degrades significantly with increased logical complexity, with models showing consistent bias toward true-labeled tasks over false or unknown ones.

AINeutralarXiv – CS AI · Jun 96/10
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Standpoint Logics with Defeasible Beliefs

This paper integrates defeasible logic with standpoint logic to formally model knowledge across multiple contradictory viewpoints that may hold uncertain beliefs. The work provides theoretical foundations for Defeasible Restricted Standpoint Logics (DRSL) and proves that computational complexity remains unchanged when extending propositional KLM entailment relations to multi-standpoint settings.

AINeutralarXiv – CS AI · Jun 25/10
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An Abstract Worlds Semantic Framework for Belief Change Operators

Researchers propose Abstract Worlds Semantics (AWS), a set-theoretic framework for modeling belief change operators without assuming logical syntax. The framework unifies classical and non-prioritized belief change constructions, providing a homogeneous account of AGM, KM, and Multiple Change models in propositional logic.

AINeutralarXiv – CS AI · Jun 15/10
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Choosing the Lens: Strategic Perspective Activation in Context-Dependent Argumentation

Researchers introduce context-dependent argumentation frameworks (CDAFs) extending Dung's argumentation theory to capture strategic manipulation of argument validity across different contexts. The framework models how an agent can selectively activate relevant criteria to influence which arguments succeed, introducing a new decision problem called ACTIVATION-MANIPULATION with unexplored complexity bounds.

AINeutralarXiv – CS AI · May 116/10
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Abductive Reasoning with Probabilistic Commonsense

Researchers propose PACS, a probabilistic framework for abductive reasoning that models how commonsense beliefs vary across individuals rather than assuming universal agreement. By combining LLMs with formal solvers to sample diverse proofs and aggregate conclusions, PACS outperforms existing reasoning approaches on multiple benchmarks, addressing a fundamental limitation in neurosymbolic AI systems.

AINeutralarXiv – CS AI · Apr 146/10
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Neuro-Symbolic Strong-AI Robots with Closed Knowledge Assumption: Learning and Deductions

This academic paper proposes a neuro-symbolic approach for AGI robots combining neural networks with formal logic reasoning using Belnap's 4-valued logic system. The framework enables robots to handle unknown information, inconsistencies, and paradoxes while maintaining controlled security through axiom-based logic inference.

AINeutralarXiv – CS AI · Apr 106/10
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Consistency-Guided Decoding with Proof-Driven Disambiguation for Three-Way Logical Question Answering

Researchers present CGD-PD, a test-time decoding method that improves large language models' performance on three-way logical question answering (True/False/Unknown) by enforcing negation consistency and resolving epistemic uncertainty through targeted entailment probes. The approach achieves up to 16% relative accuracy improvements on the FOLIO benchmark while reducing spurious Unknown predictions.

AIBullisharXiv – CS AI · Mar 166/10
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Delta1 with LLM: symbolic and neural integration for credible and explainable reasoning

Researchers introduce Delta1, a framework that integrates automated theorem generation with large language models to create explainable AI reasoning. The system combines formal logic rigor with natural language explanations, demonstrating applications across healthcare, compliance, and regulatory domains.

AINeutralarXiv – CS AI · Mar 94/10
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Aggregative Semantics for Quantitative Bipolar Argumentation Frameworks

Researchers introduce a new family of gradual semantics called aggregative semantics for Quantitative Bipolar Argumentation Frameworks (QBAF) in AI systems. The approach uses a three-stage computation that separately aggregates attackers and supporters before combining them with argument weights, providing more interpretable and parametrisable AI reasoning systems.

AINeutralarXiv – CS AI · Jun 233/10
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Study on Quantitative Dynamic Epistemic Logic for Belief Revision

This academic paper presents a formal framework for belief revision using quantitative dynamic epistemic logic (DEL), extending AGM theory to capture degrees of conviction rather than binary belief states. The research formalizes belief revision processes within a modal logic system and proposes a new revision function that better aligns with philosophical intuitions behind AGM postulates.

AINeutralarXiv – CS AI · Mar 24/107
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A Reduction of Input/Output Logics to SAT

Researchers have developed an automation approach for Input/Output (I/O) Logics, a type of deontic logic used for reasoning about norms and obligations, by reducing them to propositional satisfiability problems. A prototype implementation called 'rio' (reasoner for input/output logics) has been created to demonstrate these procedures with practical examples.