相关论文: Extending Nunchaku to Dependent Type Theory

Natural language explanation in visual question answer (VQA-NLE) aims to explain the decision-making process of models by generating natural language sentences to increase users' trust in the black-box systems. Existing post-hoc methods…

In the wake of responsible AI, interpretability methods, which attempt to provide an explanation for the predictions of neural models have seen rapid progress. In this work, we are concerned with explanations that are applicable to natural…

Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…

This paper explores the task of leveraging typology in the context of cross-lingual dependency parsing. While this linguistic information has shown great promise in pre-neural parsing, results for neural architectures have been mixed. The…

We describe the categorical semantics for a simply typed variant and a simplified dependently typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent…

Large language models make remarkable progress in reasoning capabilities. Existing works focus mainly on deductive reasoning tasks (e.g., code and math), while another type of reasoning mode that better aligns with human learning, inductive…

The expressiveness of dependent type theory can be extended by identifying types modulo some additional computation rules. But, for preserving the decidability of type-checking or the logical consistency of the system, one must make sure…

Kuroda's translation embeds classical first-order logic into intuitionistic logic, through the insertion of double negations. Recently, Brown and Rizkallah extended this translation to higher-order logic. In this paper, we adapt it for…

Higher-derivative analogues of multidimensional conformal particle and many-body conformal mechanics are constructed. Their Newton-Hooke counterparts are derived by applying appropriate coordinate transformations.

We examine the relationship between Dependence Logic and game logics. A variant of Dynamic Game Logic, called Transition Logic, is developed, and we show that its relationship with Dependence Logic is comparable to the one between…

We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…

In dependent type theory, being able to refer to a type universe as a term itself increases its expressive power, but requires mechanisms in place to prevent Girard's paradox from introducing logical inconsistency in the presence of…

Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract…

An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…

We present a tool for reasoning in and about propositional sequent calculi. One aim is to support reasoning in calculi that contain a hundred rules or more, so that even relatively small pen and paper derivations become tedious and error…

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two…

We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…

We have developed an alternative approach to teaching computer science students how to prove. First, students are taught how to prove theorems with the Coq proof assistant. In a second, more difficult, step students will transfer their…

A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…

We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\alpha), where \alpha is a Boolean variable. Intuitively, with Boolean dependence…