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We present a completeness result for a logical system which combines stit logic and justification logic in order to represent proving activity of the agents. This logic is interpreted over the semantics introduced in earlier publications.…

Logic · Mathematics 2017-07-12 Grigory Olkhovikov

A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…

Logic in Computer Science · Computer Science 2010-08-19 Robin Adams , Zhaohui Luo

In this paper, we consider a stabilization problem of a generalized thermoelastic system (the so called $\alpha-\beta$ system) with delay in a part of the coupled system. For each case, we prove the well-posedness of the corresponding…

Analysis of PDEs · Mathematics 2024-07-29 Kaïs Ammari , Makrem Salhi , Farhat Shel

In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.

Classical Analysis and ODEs · Mathematics 2020-04-08 Arpan Sadhukhan

We start by presenting a theory of finite sets using the approach which is essentially that taken by Whitehead and Russell in Principia Mathematica}, and which does not involve the natural numbers (or any other infinite set). This theory is…

History and Overview · Mathematics 2010-06-22 Chris Preston

Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.

History and Overview · Mathematics 2023-11-28 Zoltán Szilasi

McFadden and Richter (1991) and later McFadden (2005) show that the Axiom of Revealed Stochastic Preference characterizes rationalizability of choice probabilities through random utility models on finite universal choice spaces. This note…

Theoretical Economics · Economics 2019-02-21 Jörg Stoye

After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility…

General Topology · Mathematics 2014-10-27 Boris Šobot

Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that $T$ has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of…

Logic · Mathematics 2026-02-24 Predrag Tanović

We introduce the calculus of Classical Transitions (CT), which extends the research line on the relationship between linear logic and processes to labelled transitions. The key twist from previous work is registering parallelism in typing…

Logic in Computer Science · Computer Science 2018-03-06 Fabrizio Montesi , Marco Peressotti

In [ABM07], Abdulla et al. introduced the concept of decisiveness, an interesting tool for lifting good properties of finite Markov chains to denumerable ones. Later, this concept was extended to more general stochastic transition systems…

Logic in Computer Science · Computer Science 2020-09-24 Patricia Bouyer , Thomas Brihaye , Mickael Randour , Cédric Rivière , Pierre Vandenhove

We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…

Logic · Mathematics 2021-11-02 Juvenal Murwanashyaka

In this paper, we present two methods to provide explanations for reasoning with belief functions in the valuation-based systems. One approach, inspired by Strat's method, is based on sensitivity analysis, but its computation is simpler…

Artificial Intelligence · Computer Science 2013-02-21 Hong Xu , Philippe Smets

Event Structures (ESs) are mainly concerned with the representation of causal relationships between events, usually accompanied by other event relations capturing conflicts and disabling. Among the most prominent variants of ESs are Prime…

Logic in Computer Science · Computer Science 2013-07-30 Youssef Arbach , Kirstin Peters , Uwe Nestmann

Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that…

History and Philosophy of Physics · Physics 2021-06-16 Harvey R. Brown

The connections among natural language processing and argumentation theory are becoming stronger in the latest years, with a growing amount of works going in this direction, in different scenarios and applying heterogeneous techniques. In…

Artificial Intelligence · Computer Science 2014-05-06 Elena Cabrio , Serena Villata

We propose a novel approach to logic-based learning which generates assumption-based argumentation (ABA) frameworks from positive and negative examples, using a given background knowledge. These ABA frameworks can be mapped onto logic…

Artificial Intelligence · Computer Science 2023-05-26 Maurizio Proietti , Francesca Toni

The axiomatic system introduced by H\'ajek axiomatizes first-order logic based on BL-chains. In this study, we extend this system with the axiom $(\forall x \phi)^2 \leftrightarrow \forall x \phi^2$ and the infinitary rule \[ \frac{\phi…

Logic · Mathematics 2024-08-12 Diego Castaño , José Patricio Díaz Varela , Gabriel Savoy

We show how to attach to any stratum of a reductive group a (small) finite group. We also show that in the simply laced case the set of strata is in bijection with a subset of the set of almost special representations of the Weyl group.…

Representation Theory · Mathematics 2024-09-25 G. Lusztig

In this article, we present a novel approach for parsing argumentation structures. We identify argument components using sequence labeling at the token level and apply a new joint model for detecting argumentation structures. The proposed…

Computation and Language · Computer Science 2016-07-25 Christian Stab , Iryna Gurevych