Related papers: Foundations for abstract forcing
In this paper, we present a general framework for ranking sets of arguments in abstract argumentation based on their plausibility of acceptance. We present a generalisation of Dung's extension semantics as extension-ranking semantics, which…
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add…
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…
The aim of this paper is to generalize a main theorem concerning weighted mean summability to absolute matrix summability which plays a vital role in summability theory and applications to the other sciences by using quasi-$f$-power…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance…
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of…
We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…
A theoretical model is presented which provides a way to simulate, at a very abstract level, power struggles in the social world. In the model, agents can benefit or harm each other, to varying degrees and with differing levels of…
In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with…
We define typical forcings encompassing many informal forcing arguments in bounded arithmetic and give general conditions for such forcings to produce models of the universal variant of relativized $T^1_2$. We apply this result to study the…
We present the foundational theory of condensed sets and basic condensed algebra after having introduced key concepts from category theory and homological algebra. In the later sections, we indicate the relevance of condensed mathematics to…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel…
Recently interest in using generalized reductions to construct massive supergravity theories has been revived in the context of M-theory and superstring theory. These compactifications produce mass parameters by introducing a linear…