arXiv subjects

Ziba Assadi

Publications and source records attributed to Ziba Assadi.

5 recordsLinked to original sources

arXiv2026

Fuzzy Representation of Norms

Autonomous systems (AS) powered by AI components are increasingly integrated into the fabric of our daily lives and society, raising concerns about their ethical and social impact. To be considered trustworthy, AS must adhere to ethical principles and values. This has led to significant research on the identification and incorporation of ethical requirements in AS system design. A recent development in this area is the introduction of SLEEC (Social, Legal, Ethical, Empathetic, and Cultural) rules, which provide a comprehensive framework for representing ethical and other normative considerations. This paper proposes a logical representation of SLEEC rules and presents a methodology to embed these ethical requirements using test-score semantics and fuzzy logic. The use of fuzzy logic is motivated by the view of ethics as a domain of possibilities, which allows the resolution of ethical dilemmas that AI systems may encounter. The proposed approach is illustrated through a case study.

cs.AI↗

arXiv2024

On Representing Humans' Soft-Ethics Preferences As Dispositions

The aim of this paper is to represent humans' soft-ethical preferences by means of dispositional properties. We begin by examining real-life situations, termed as scenarios, that involve ethical dilemmas. Users engage with these scenarios, making decisions on how to act and providing justifications for their choices. We adopt a dispositional approach to represent these scenarios and the interaction with the users. Dispositions are properties that are instantiated by any kind of entity and that may manifest if properly triggered. In particular, the dispositional properties we are interested in are the ethical and behavioural ones. The approach will be described by means of examples. The ultimate goal is to implement the results of this work into a software exoskeleton solution aimed at augmenting human capabilities by preserving their soft-ethical preferences in interactions with autonomous systems.

cs.HC↗

arXiv2020

Decidability of the Multiplicative and Order Theory of Numbers

The ordered structures of natural, integer, rational and real numbers are studied in this thesis. The theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order and addition are decidable and infinitely axiomatizable. For the language of order and multiplication, it is known that the theories of $\mathbb{N}$ and $\mathbb{Z}$ are not decidable (and so not axiomatizable by any computably enumerable set of sentences). By Tarski's theorem, the multiplicative ordered structure of $\mathbb{R}$ is decidable also. In this thesis we prove this result directly by quantifier elimination and present an explicit infinite axiomatization. The structure of $\mathbb{Q}$ in the language of order and multiplication seems to be missing in the literature. We show the decidability of its theory by the technique of quantifier elimination and after presenting an infinite axiomatization for this structure, we prove that it is not finitely axiomatizable.

math.LO↗

arXiv2020

On the Truth of Gödelian and Rosserian Sentences

There is a longstanding debate in the logico-philosophical community as to why the Gödelian sentences of a consistent and sufficiently strong theory are true. The prevalent argument seems to be something like this: since every one of the Gödelian sentences of such a theory is equivalent to the theory's consistency statement, even provably so inside the theory, the truth of those sentences follows from the consistency of the theory in question. So, Gödelian sentences of consistent theories should be true. In this paper, we show that Gödelian sentences of only sound theories are true; and there is a long road from consistency to soundness, indeed a hierarchy of conditions which are satisfied by some theories and falsified by others. We also study the truth of Rosserian sentences and provide necessary and sufficient conditions for the truth of Rosserian (and also Gödelian) sentences of theories.

math.LO↗

arXiv2018

On Decidability of the Ordered Structures of Numbers

The ordered structures of natural, integer, rational and real numbers are studied here. It is known that the theories of these numbers in the language of order are decidable and finitely axiomatizable. Also, their theories in the language of order and addition are decidable and infinitely axiomatizable. For the language of order and multiplication, it is known that the theories of $\mathbb{N}$ and $\mathbb{Z}$ are not decidable (and so not axiomatizable by any computably enumerable set of sentences). By Tarski's theorem, the multiplicative ordered structure of $\mathbb{R}$ is decidable also; here we prove this result directly and present an axiomatization. The structure of $\mathbb{Q}$ in the language of order and multiplication seems to be missing in the literature; here we show the decidability of its theory by the technique of quantifier elimination and after presenting an infinite axiomatization for this structure we prove that it is not finitely axiomatizable.

math.LO↗