相关论文: Restricted Rules of Inference and Paraconsistency

Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…

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…

Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…

This paper investigates the problem of inferring knowledge from data so that the inferred knowledge is interpretable and informative to humans who have prior knowledge. Given a dataset as a collection of system trajectories, we infer…

A non-distributive two-sorted hypersequent calculus \textbf{PDBL} and its modal extension \textbf{MPDBL} are proposed for the classes of pure double Boolean algebras and pure double Boolean algebras with operators respectively. A relational…

This Paper investigate sequent calculi for certain weak subintuitionistic logics. We establish that weakening and contraction are height-preserving admissible for each of these calculi, and we provide a syntactic proof for the admissibility…

Real-valued logics have seen a renewed interest in verification for probabilistic and quantitative systems, in particular machine learning models, where they can be used to directly integrate specifications in the training objective. To do…

Probabilistic Logic Programming (PLP) languages, like ProbLog, naturally support reasoning under uncertainty, while maintaining a declarative and interpretable framework. Meanwhile, counterfactual reasoning (i.e., answering ``what if''…

Recent studies demonstrated that large language models (LLMs) can excel in many tasks via in-context learning (ICL). However, recent works show that ICL-prompted models tend to produce inaccurate results when presented with adversarial…

Mainstream methods for Legal Judgment Prediction (LJP) based on Pre-trained Language Models (PLMs) heavily rely on the statistical correlation between case facts and judgment results. This paradigm lacks explicit modeling of legal…

Deep Reinforcement Learning (RL) is remarkably effective in addressing sequential resource allocation problems in domains such as healthcare, public policy, and resource management. However, deep RL policies often lack transparency and…

Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…

One important challenge for probabilistic logics is reasoning with very large knowledge bases (KBs) of imperfect information, such as those produced by modern web-scale information extraction systems. One scalability problem shared by many…

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…

Lifted inference has been proposed for various probabilistic logical frameworks in order to compute the probability of queries in a time that depends on the size of the domains of the random variables rather than the number of instances.…

The semantics of the Prolog ``cut'' construct is explored in the context of some desirable properties of logic programming systems, referred to as the witness properties. The witness properties concern the operational consistency of…

We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…

In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…

Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…

Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…