Related papers: IST is more than an algorithm to prove ZFC theorem…

We introduce incongruent normal form (INF), a structural representation for self-referential semantic sentences. An INF replaces a self-referential sentence with a finite family of non-self-referential sentences that are individually…

Neural machine translation (NMT), a new approach to machine translation, has achieved promising results comparable to those of traditional approaches such as statistical machine translation (SMT). Despite its recent success, NMT cannot…

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…

This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…

Over the past decade a considerable amount of research has been done to expand logic programming languages to handle incomplete information. One such language is the language of epistemic specifications. As is usual with logic programming…

End-to-end neural machine translation has overtaken statistical machine translation in terms of translation quality for some language pairs, specially those with large amounts of parallel data. Besides this palpable improvement, neural…

Church's Higher Order Logic is a basis for influential proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of…

In neural machine translation (NMT), the computational cost at the output layer increases with the size of the target-side vocabulary. Using a limited-size vocabulary instead may cause a significant decrease in translation quality. This…

We study the properties of the language of Stratified Sets (first-order logic with $\in$ and a stratification condition) as used in TST, TZT, and (with stratifiability instead of stratification) in Quine's NF. We find that the syntax forms…

In this paper, we present full models for some Paraconsistent Set Theories (PSTs). These models are built over Fidel semantics where they are specific first-order structures in the sense of Model Theory. These structures are known as…

Sentence embedding methods using natural language inference (NLI) datasets have been successfully applied to various tasks. However, these methods are only available for limited languages due to relying heavily on the large NLI datasets. In…

Current Natural Language Inference (NLI) systems primarily operate at the sentence level, providing black-box decisions that lack explanatory power. While atomic-level NLI offers a promising alternative by decomposing hypotheses into…

We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…

There have been many successful applications of sentence embedding methods. However, it has not been well understood what properties are captured in the resulting sentence embeddings depending on the supervision signals. In this paper, we…

Word sense induction (WSI) is the task of unsupervised clustering of word usages within a sentence to distinguish senses. Recent work obtain strong results by clustering lexical substitutes derived from pre-trained RNN language models…

In many applications, it is important to be able to explain the decisions of machine learning systems. An increasingly popular approach has been to seek to provide \emph{counterfactual instance explanations}. These specify close possible…

Set Matrix Theory (SMT) has been introduced in Log. Anal. 225: 59-82 (2014) as a generalization of ZF, in which matrices constructed from sets are treated as urelements, that is, as objects that are not sets but that can be elements of…

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics…

Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…

An AIA formula is one of the form 'A implies B' where A and B are purely universal. Up to a simple reduction AIA formula are both EA and AE. In an earlier paper Solovay, Harrison and I proved the undecidability of validity for the AIA…