Related papers: Encoding impredicative hierarchy of type universes…
We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. We prove some basic properties of the calculus, such as normalisation and the subformula property and also…
We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Argumentation frameworks ($AF$s) have been a useful tool for approximate reasoning. The encoding method is an important approach to formally model $AF$s under related semantics. The aim of this paper is to develop the encoding method from…
Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much…
In this paper we propose an approach to reasoning about properties of imperative programs. We assume in this context that the meanings of program constructs are described using rules in the natural semantics style with the additional…
The integration of lexical semantics and pragmatics in the analysis of the meaning of natural lan- guage has prompted changes to the global framework derived from Montague. In those works, the original lexicon, in which words were assigned…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
Parametricity allows the transfer of proofs between different implementations of the same data structure. The lambdaPi-calculus modulo theory is an extension of the lambda-calculus with dependent types and user-defined rewrite rules. It is…
Logical reasoning over incomplete knowledge graphs to answer complex logical queries is a challenging task. With the emergence of new entities and relations in constantly evolving KGs, inductive logical reasoning over KGs has become a…