Related papers: Syntactic Forcing Models for Coherent Logic

We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional systems: Our syntactical separation…

The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…

In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for…

Despite the success of language models using neural networks, it remains unclear to what extent neural models have the generalization ability to perform inferences. In this paper, we introduce a method for evaluating whether neural models…

We focus on the production of efficient descriptions of objects, actions and events. We define a type of efficiency, textual economy, that exploits the hearer's recognition of inferential links to material elsewhere within a sentence.…

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…

This paper explores whether language models can effectively resolve the complex binding patterns of the Mandarin Chinese reflexive ziji, which are constrained by both syntactic and semantic factors. We construct a dataset of 240 synthetic…

An important characteristic of many logics for Artificial Intelligence is their nonmonotonicity. This means that adding a formula to the premises can invalidate some of the consequences. There may, however, exist formulae that can always be…

In this paper we provide a unifying description of different types of semantics of modal logic found in the literature via the framework of topological categories. In the style of categorical logic, we establish an exact correspondence…

The paper presents a language model that develops syntactic structure and uses it to extract meaningful information from the word history, thus enabling the use of long distance dependencies. The model assigns probability to every joint…

I deal with two approaches to proof-theoretic semantics: one based on argument structures and justifications, which I call reducibility semantics, and one based on consequence among (sets of) formulas over atomic bases, called base…

We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…

The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.

Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…

Sentence embedding is an important research topic in natural language processing. It is essential to generate a good embedding vector that fully reflects the semantic meaning of a sentence in order to achieve an enhanced performance for…

We present a general relational semantics framework which, by varying the axiomatization and components of the relational structures, provides a uniform semantics for sentential logics, classical and non-classical alike. The approach we…

Syntactic parsing is the task of assigning a syntactic structure to a sentence. There are two popular syntactic parsing methods: constituency and dependency parsing. Recent works have used syntactic embeddings based on constituency trees,…

Text-to-image (T2I) models enable rapid concept design, making them widely used in AI-driven design. While recent studies focus on generating semantic and stylistic variations of given design concepts, functional coherence--the integration…

This is an introduction to the set-theoretic method of forcing, including its application in proving the independence of the Continuum Hypothesis from the Zermelo-Fraenkel axioms of set theory. I presuppose no particular mathematical…

We develop a classical propositional logic for reasoning about combinatory logic. We define its syntax, axiomatic system and semantics. The syntax and axiomatic system are presented based on classical propositional logic, with typed…