Related papers: A Tableaux Calculus for Ambiguous Quantification
The capture calculus is an extension of System F<: that tracks free variables of terms in their type, allowing one to represent capabilities while limiting their scope. While previous calculi had mechanized soundness proofs -- notably…
We cast aspects of consciousness in axiomatic mathematical terms, using the graphical calculus of general process theories (a.k.a symmetric monoidal categories and Frobenius algebras therein). This calculus exploits the ontological…
I explore some of the issues that arise when trying to establish a connection between the underspecification hypothesis pursued in the NLP literature and work on ambiguity in semantics and in the psychological literature. A theory of…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
We consider the problem of disambiguating the lemma and part of speech of ambiguous words in morphologically rich languages. We propose a method for disambiguating ambiguous words in context, using a large un-annotated corpus of text, and a…
Reliable uncertainty quantification is a first step towards building explainable, transparent, and accountable artificial intelligent systems. Recent progress in Bayesian deep learning has made such quantification realizable. In this paper,…
We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction. This construction works well for…
Reasoning about tabular information presents unique challenges to modern NLP approaches which largely rely on pre-trained contextualized embeddings of text. In this paper, we study these challenges through the problem of tabular natural…
Despite extensive research on textual and visual disambiguation, disambiguation through speech (DTS) remains underexplored. This is largely due to the lack of high-quality datasets that pair spoken sentences with richly ambiguous text. To…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…
In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
Specification languages are essential in deductive program verification, but they are usually based on first-order logic, hence less expressive than the programs they specify. Recently, trace specification logics with fixed points that are…
I review evidence for the claim that syntactic ambiguities are resolved on the basis of the meaning of the competing analyses, not their structure. I identify a collection of ambiguities that do not yet have a meaning-based account and…
The classical lambda calculus may be regarded both as a programming language and as a formal algebraic system for reasoning about computation. It provides a computational model equivalent to the Turing machine, and continues to be of…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension,…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…