Related papers: Frege on the reference of sentences

Using Heijenoort's unpublished generalized rules of quantification, we discuss the proof of Herbrand's Fundamental Theorem in the form of Heijenoort's correction of Herbrand's "False Lemma" and present a didactic example. Although we are…

While paragraph embedding models are remarkably effective for downstream classification tasks, what they learn and encode into a single vector remains opaque. In this paper, we investigate a state-of-the-art paragraph embedding method…

In this paper a class of languages which are formal enough for mathematical reasoning is introduced. First-order formal languages containing natural numbers and numerals belong to that class. Its languages are called mathematically…

This is a study of S. Kripke's notion of fulfilment. Motivated by Paris-Harrington statement, Kripke was looking for a proof of G\"odel's Incompleteness Theorem which was model-theoretic, natural (without self-reference), and easy.…

This paper gives a counterexample to the impossibility, by G\"odel's second incompleteness theorem, of proving a formula expressing the consistency of arithmetic in a fragment of arithmetic on the assumption that the latter is consistent.…

We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.

Towards better explainability in the field of information retrieval, we present CREDENCE, an interactive tool capable of generating counterfactual explanations for document rankers. Embracing the unique properties of the ranking problem, we…

Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…

In a recent article, Brette argues that coding as a concept is inappropriate for explanations of neurocognitive phenomena. Here, we argue that Brette's conceptual analysis mischaracterizes the structure of causal claims in coding and other…

The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it appears as a…

Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…

The strength with which a statement is made can have a significant impact on the audience. For example, international relations can be strained by how the media in one country describes an event in another; and papers can be rejected…

This paper explores proof-theoretic semantics, a formal approach to inferential semantics. It derives sentence meaning from formalized proofs, building upon Gentzen and Prawitz's work. The study addresses challenges in understanding how…

We study self-referential sentences of the type related to the Liar paradox. In particular, we consider the problem of assigning consistent fuzzy truth values to collections of self-referential sentences. We show that the problem can be…

Every countable language which conforms to classical logic is shown to have an extension which conforms to classical logic, and has a definitional theory of truth. That extension has a semantical theory of truth, if every sentence of the…

Bernays introduced a method for proving underivability results in propositional calculi by truth tables. In general, this motivates an investigations of how to find, given a propositional logic, a finite-valued logic which has as few…

We present a new English translation of L.E.J. Brouwer's paper `De onbetrouwbaarheid der logische principes' (The unreliability of the logical principles) of 1908, together with a philosophical and historical introduction. In this paper…

Despite the syntactic fluency of Large Language Models (LLMs), ensuring their logical correctness in high-stakes domains remains a fundamental challenge. We present a neurosymbolic framework that combines LLMs with SMT solvers to produce…

Using techniques developed in the revision theory of truth, I build a model for the set theory NF (New Foundations) developed by Quine in ZF, therefore proving its consistency relative to ZF. The model is essentially a term model; the sets…

Recent advancements in text summarization, particularly with the advent of Large Language Models (LLMs), have shown remarkable performance. However, a notable challenge persists as a substantial number of automatically-generated summaries…