相关论文: A Simplified Variant of G\"odel's Ontological Argu…

The ability to conduct logical reasoning is a fundamental aspect of intelligent human behavior, and thus an important problem along the way to human-level artificial intelligence. Traditionally, logic-based symbolic methods from the field…

We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one…

We present an extension-based approach for computing and verifying preferences in an abstract argumentation system. Although numerous argumentation semantics have been developed previously for identifying acceptable sets of arguments from…

We show that the sheer existence of a quantum computational speedup logically implies the mutually exclusive or of well-defined causal loops. In each of them, it is as if the problem-solver knew in advance one of the possible halves of the…

Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…

We introduce ontology-mediated planning, in which planning problems are combined with an ontology. Our formalism differs from existing ones in that we focus on a strong separation of the formalisms for describing planning problems and…

We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut…

We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…

An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…

Explainable Artificial Intelligence and Formal Argumentation have received significant attention in recent years. Argumentation-based systems often lack explainability while supporting decision-making processes. Counterfactual and…

Analogy has been shown to be important in many key cognitive abilities, including learning, problem solving, creativity and language change. For cognitive models of analogy, the fundamental computational question is how its inherent…

G{\"o}del's completeness theorem for classical first-order logic is one of the most basic theorems of logic. Central to any foundational course in logic, it connects the notion of valid formula to the notion of provable formula.We survey a…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…

This is an examination, a commentary, of links between some philosophical views ascribed to G\"odel and general proof theory. In these views deduction is of central concern not only in predicate logic, but in set theory too, understood from…

By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…

Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…

This paper is devoted to systematic studies of some extensions of first-order G\"odel logic. The first extension is the first-order rational G\"odel logic which is an extension of first-order G\"odel logic, enriched by countably many…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

How can we reason around logical paradoxes without falling into them? This paper introduces grounded deduction or GD, a Kripke-inspired approach to first-order logic and arithmetic that is neither classical nor intuitionistic, but…

We introduce a syntactic translation of Goedel's System T parametrized by a weak notion of a monad, and prove a corresponding fundamental theorem of logical relation. Our translation structurally corresponds to Gentzen's negative…