Related papers: Normalization by gluing for free {\lambda}-theorie…
We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is…
Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
We present a framework for deriving inference relations between Dutch sentence pairs. The proposed framework relies on logic-based reasoning to produce inspectable proofs leading up to inference labels; its judgements are therefore…
We have previously published the Isabelle/HOL formalization of a general theory of syntax with bindings. In this companion paper, we instantiate the general theory to the syntax of lambda-calculus and formalize the development leading to…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
Riddles based on simple puns can be classified according to the patterns of word, syllable or phrase similarity they depend upon. We have devised a formal model of the semantic and syntactic regularities underlying some of the simpler types…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the $\invertediota$ operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…
We present a framework for the formal meta-theory of lambda calculi in first-order syntax, with two sorts of names, one to represent both free and bound variables, and the other for constants, and by using Stoughton's multiple…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
We uncover a close relationship between combinatorial and syntactic proofs for first-order logic (without equality). Whereas syntactic proofs are formalized in a deductive proof system based on inference rules, a combinatorial proof is a…
Word embeddings carry stereotypical connotations from the text they are trained on, which can lead to invalid inferences in downstream models that rely on them. We use this observation to design a mechanism for measuring stereotypes using…
Since the seminal work of J. A. Robinson on resolution, many lifting lemmas for simplifying proofs of completeness of resolution have been proposed in the literature. In the logic programming framework, they may also help to detect some…