Related papers: A Revision Theoretic Model for NF
We determine the modal logic of fixed-point models of truth and their axiomatizations by Solomon Feferman via Solovay-style completeness results. Given a fixed-point model $\mathcal{M}$, or an axiomatization $S$ thereof, we find a modal…
If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are characterized when M is countable and arithmetically…
In this paper we provide a detailed construction of an equivalence between the category of Lawvere theories and the category of relative monads on the obvious functor $Jf:F\rightarrow Sets$ where $F$ is the category with the set of objects…
A reinforcement learning algorithm accomplishes the task of synthesizing a set-theoretical formula that evaluates to given truth values for given assignments.
It is generally well agreed that developing a unifying theory is one of the most important issues in Data Mining research. In the last two decades, a great deal of work has been devoted to the algorithmic aspects of the Frequent Itemset…
Guaranteeing the correctness and factuality of language model (LM) outputs is a major open problem. In this work, we propose conformal factuality, a framework that can ensure high probability correctness guarantees for LMs by connecting…
Transformer-based language models are effective but complex, and understanding their inner workings and reasoning mechanisms is a significant challenge. Previous research has primarily explored how these models handle simple tasks like name…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
ZF is a well investigated impredicative constructive version of Zermelo-Fraenkel set theory. Using set terms, we axiomatize IZF with Replacement, which we call \izfr, along with its intensional counterpart \iizfr. We define a typed lambda…
Despite advancements in large language models (LLMs), non-factual responses still persist in fact-seeking question answering. Unlike extensive studies on post-hoc detection of these responses, this work studies non-factuality prediction…
Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much…
Modeling the structure of coherent texts is a key NLP problem. The task of coherently organizing a given set of sentences has been commonly used to build and evaluate models that understand such structure. We propose an end-to-end…
We propose a nested recurrent neural network (nested RNN) model for English spelling error correction and generate pseudo data based on phonetic similarity to train it. The model fuses orthographic information and context as a whole and is…
There are now many explainable AI methods for understanding the decisions of a machine learning model. Among these are those based on counterfactual reasoning, which involve simulating features changes and observing the impact on the…
Evaluating an explanation's faithfulness is desired for many reasons such as trust, interpretability and diagnosing the sources of model's errors. In this work, which focuses on the NLI task, we introduce the methodology of…
We provide a semi-grammatical description of the set of normal proofs of positive formulae in minimal predicate logic, i.e. a grammar that generates a set of schemes, from each of which we can produce a finite number of normal proofs. This…
The predominant success of diffusion models in generative modeling has spurred significant interest in understanding their theoretical foundations. In this work, we propose a feature learning framework aimed at analyzing and comparing the…
In this paper we show that the intuitionistic fixed point theory FiX^{i}(X) over set theories T is a conservative extension of T if T can manipulate finite sequences and has the full foundation schema.
Let V be the universe of sets and V_{\alpha} the sets of rank \leq\alpha. We develop some axiom schemata for set theory based on the following three assumptions: 1. V \models ZFC 2. V is large with respect to the class of ordinals 3. V is…
Pretrained language models (PLMs) based knowledge-grounded dialogue systems are prone to generate responses that are factually inconsistent with the provided knowledge source. In such inconsistent responses, the dialogue models fail to…