Related papers: On Constructive Axiomatic Method
End-to-end dialogue generation has achieved promising results without using handcrafted features and attributes specific for each task and corpus. However, one of the fatal drawbacks in such approaches is that they are unable to generate…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…
Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms.…
The reproducibility of scientific articles is central to the advancement of science. Despite this importance, evaluating reproducibility remains challenging due to the scarcity of ground truth data. Predictive models can address this…
Various methods have been used to construct rational points and rational curves on rationally connected algebraic varieties. We survey recent advances in two of them, the descent and the fibration method, in a number-theoretical context…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
The evaluation of narrative quality remains a complex challenge, as it involves subjective factors such as plot, character development, and emotional impact. This work proposes a quantitative approach to narrative assessment by focusing on…
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
From this set of procedures for given clause we shall choose only interrogation of experts on pairs decisions. It is widely widespread method. It makes the whole chapter in the theory of the decision-making, well investigated with the…
This paper studies choice situations in which a decision maker can choose multiple alternatives. Given a menu of available options, the decision maker selects a subset of the menu with certain probabilities. We employ an axiomatic approach…
We give here a constructive account of the frequentist approach to probability, by means of natural density. Using this notion of natural density, we introduce some probabilistic versions of the Limited Principle of Omniscience. Finally we…
In this preprint, we present A collaborative human-AI approach to building an inspectable semantic layer for Agentic AI. AI agents first propose candidate knowledge structures from diverse data sources; domain experts then validate,…
This paper from 2008 is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the foundations are laid for later results. These foundations consist of a thorough…
To date, most probabilistic reasoning systems have relied on a fixed belief network constructed at design time. The network is used by an application program as a representation of (in)dependencies in the domain. Probabilistic inference…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability…
We provide a "shared axiomatization" of natural numbers and hereditarily finite sets built around a polymorphic abstraction of bijective base-2 arithmetics. The "axiomatization" is described as a progressive refinement of Haskell type…