In this paper we present some of our school’s results in the area of building up relativity theory (RT) as a hierarchy of theories in the sense of logic. We use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and we build on experience gained in FOM. The main aims of our school are the following: We want to base the theory on simple, unambiguous axioms with clear meaning...

Carruthers (2000; 2005) provides a general defence of reductive representationalism about phenomenal consciousness while critiquing first-order theories of the sort proposed by Baars (1988), Tye (1995), Dennett (2001), and others (thereby motivating a form of higher-order account). The present paper defends first-order theories against that attack.

We expand the notion of resplendency to theories of the kind T + p↑, where T is a first-order theory and p↑ expresses that the type p is omitted. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author’s doctoral thesis [3].

With the fast evolvement of embedded deep-learning computing systems, applications powered by deep learning are moving from cloud to edge. When deploying neural networks (NNs) onto devices under complex environments, there various types possible faults: soft errors caused cosmic radiation and radioactive impurities, voltage instability, aging, temperature variations, malicious attackers, so on....

This paper presents a theory of informative communications among agents that allows a speaker to communicate to a hearer truths about the state of the world; the occurrence of events, including other communicative acts; and the knowledge states of any agent — speaker, hearer, or third parties — any of these in the past, present, or future — and any logical combination of these, including formul...

In a recent meta-analysis, Khemlani & Johnson-Laird (2012) showed that the conclusions drawn by human reasoners in psychological experiments about syllogistic reasoning are not the conclusions predicted by classical first-order logic. Moreover, current cognitive theories deviate significantly from the empirical data. In this paper we show how human syllogistic reasoning can be modelled under th...

We prove a set-theoretic version of Hájek, Paris and Shepherdson’s theorem [HPS00] as follows: The set ω of natural numbers must contain a non-standard natural number in any natural Tarskian semantics of Cà L0(ω), the set theory with comprehension principle within à Lukasiewicz’s infinitevalued predicate logic. The key idea of the proof is a generalization of the derivation of Moh Shaw-Kwei’s p...

We give a presentation of the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan [12]. We limit our attention to a simple major subclass of V -minimal theories of the form ACVF S , that is, the theory of algebraically cl...