Related papers: An introdution to forcing
It is well known to generalize the meagre ideal replacing aleph_0 by a (regular) cardinal lambda > aleph_0 and requiring the ideal to be lambda^+-complete. But can we generalize the null ideal? In terms of forcing, this means finding a…
In the context of $\mathsf{ZF}$, we analyze a version of Hindman's finite unions theorem on infinite sets, which normally requires the Axiom of Choice to be proved. We establish the implication relations between this statement and various…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
In this paper we solve the satisfiability problem of an extended fragment of set computable theory which "forces the infinity" by a fruitful use of the witness small model property and the theory of formative processes.
We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.
The Force Concept Inventory (FCI) is a well-established physics education assessment tool used to evaluate students' comprehension of elementary mechanics principles. While it can be used to analyse the effectiveness of instruction if…
We define a $\sigma$-centered notion of forcing that forces the existence of a Boolean algebra with the Grothendieck property and without the Nikodym property. In particular the existence of such an algebra is consistent with the negation…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Machine learning presents a general, systematic framework for the generation of formal theoretical models for physical description and prediction. Tentatively standard linear modeling techniques are reviewed; followed by a brief discussion…
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…
Reinforcement Learning (RL), a subfield of Artificial Intelligence (AI), focuses on training agents to make decisions by interacting with their environment to maximize cumulative rewards. This paper provides an overview of RL, covering its…
We present a set-theoretic, proof-irrelevant model for Calculus of Constructions (CC) with predicative induction and judgmental equality in Zermelo-Fraenkel set theory with an axiom for countably many inaccessible cardinals. We use Aczel's…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary submodels of some (H(chi), in). This leads to forcing notions which are…
We introduce a simplified framework for ord-transitive models and Shelah's non elementary proper (nep) theory. We also introduce a new construction for the countable support nep iteration.
This paper presents a method for inducing logic programs from examples that learns a new class of concepts called first-order decision lists, defined as ordered lists of clauses each ending in a cut. The method, called FOIDL, is based on…
This article is a gentle discussion about the field of reinforcement learning in practice, about opportunities and challenges, touching a broad range of topics, with perspectives and without technical details. The article is based on both…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Reinforcement learning is one of the core components in designing an artificial intelligent system emphasizing real-time response. Reinforcement learning influences the system to take actions within an arbitrary environment either having…