A Deontic Stit Logic Based on Beliefs and Expected Utility

Abarca, Aldo Iván Ramírez; Broersen, Jan

doi:10.4204/eptcs.335.27

Cited by 3 publications

(15 citation statements)

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“…To clarify, over the last two decades researchers have shown that one can draw bridges between stit theory and theories such as dynamic logic (Canavotto, 2020;Herzig & Lorini, 2010;Horty, 2019;van Benthem & Pacuit, 2014), coalition logic (Broersen, Herzig, & Troquard, 2006b), § 1.2. Logic-Based Formalization of Responsibility • 11 alternating-time temporal logic (Broersen, Herzig, & Troquard, 2006a), and decision-& epistemic game theory (Abarca & Broersen, 2021a;Duijf, 2018;Tamminga, 2013), among others. Consequently, one can incorporate the concepts native to these fields into stit-theoretic analyses.…”

Section: The Toolmentioning

confidence: 99%

“…-Chapter 3 is based on my joint work with Jan Broersen (Abarca & Broersen, 2021b). Additionally, its conclusion includes a restriction of a framework that was introduced in another article with Jan Broersen (Abarca & Broersen, 2021a).…”

Section: Sources Of the Original Materialsmentioning

confidence: 99%

“…60 Now, although the stit-theory community has shown a considerable interest in exploring the influence of knowledge on agency over the last two decades, there are relatively few extensions of BST with belief modalities. To the best of my knowledge, such an extension has been previously addressed only by Wansing (2006a), by Broersen (2011c), and in my recent joint work with Jan Broersen (Abarca & Broersen, 2021a). The first study incorporated beliefs into BST to analyze the concept of doxastic voluntarism-a philosophical premise by which agents actively decide to acquire certain beliefs.…”

Section: Extension With Epistemic Notionsmentioning

confidence: 99%

“…The second one added probabilities to bt-models to represent the degrees of belief that an agent can have regarding the bringing about of some state of affairs as an effect of one of its available actions. Finally, Abarca and Broersen (2021a) picked up the connection between game theory (EGT, in particular) and act-utilitarian stit theory to explore the interplay between beliefs, agency, and obligations. In fact, the conclusions of Chapters 3,4,and 6 explore a version of this last proposal, to account for the importance of belief as a component of responsibility.…”

Section: Extension With Epistemic Notionsmentioning

confidence: 99%

“…Given the similarities between epistemic stit theory (EST) and EGT, a most natural approach to take is the probabilistic one (the third point). According to my joint work with Jan Broersen (Abarca & Broersen, 2021a), factoring a probabilistic semantics of belief into EST also paves the way for nuanced formalizations of responsibility, given that it allows to base ideas of belief-driven choice on expected-utility maximization. Since such ideas underlie the responsibilityrelated extensions of EST that are presented in the conclusions of Chapters 4 and 6, I address their basis here.…”

Section: An Extension With Beliefmentioning

confidence: 99%

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Logics of Responsibility

Abarca¹

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The study of responsibility is a complicated matter. The term is used in different ways in different fields, and it is easy to engage in everyday discussions as to why someone should be considered responsible for something. Typically, the backdrop of these discussions involves social, legal, moral, or philosophical problems. A clear pattern in all these spheres is the intent of issuing standards for when---and to what extent---an agent should be held responsible for a state of affairs. This is where Logic lends a hand. The development of expressive logics---to reason about agents' decisions in situations with moral consequences---involves devising unequivocal representations of components of behavior that are highly relevant to systematic responsibility attribution and to systematic blame-or-praise assignment. To put it plainly, expressive syntactic-and-semantic frameworks help us analyze responsibility-related problems in a methodical way. This thesis builds a formal theory of responsibility. The main tool used toward this aim is modal logic and, more specifically, a class of modal logics of action known as stit theory. The underlying motivation is to provide theoretical foundations for using symbolic techniques in the construction of ethical AI. Thus, this work means a contribution to formal philosophy and symbolic AI. The thesis's methodology consists in the development of stit-theoretic models and languages to explore the interplay between the following components of responsibility: agency, knowledge, beliefs, intentions, and obligations. Said models are integrated into a framework that is rich enough to provide logic-based characterizations for three categories of responsibility: causal, informational, and motivational responsibility. The thesis is structured as follows. Chapter 2 discusses at length stit theory, a logic that formalizes the notion of agency in the world over an indeterministic conception of time known as branching time. The idea is that agents act by constraining possible futures to definite subsets. On the road to formalizing informational responsibility, Chapter 3 extends stit theory with traditional epistemic notions (knowledge and belief). Thus, the chapter formalizes important aspects of agents' reasoning in the choice and performance of actions. In a context of responsibility attribution and excusability, Chapter 4 extends epistemic stit theory with measures of optimality of actions that underlie obligations. In essence, this chapter formalizes the interplay between agents' knowledge and what they ought to do. On the road to formalizing motivational responsibility, Chapter 5 adds intentions and intentional actions to epistemic stit theory and reasons about the interplay between knowledge and intentionality. Finally, Chapter 6 merges the previous chapters' formalisms into a rich logic that is able to express and model different modes of the aforementioned categories of responsibility. Technically, the most important contributions of this thesis lie in the axiomatizations of all the introduced logics. In particular, the proofs of soundness & completeness results involve long, step-by-step procedures that make use of novel techniques.

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Section: The Toolmentioning

confidence: 99%

Section: Sources Of the Original Materialsmentioning

confidence: 99%

Section: Extension With Epistemic Notionsmentioning

confidence: 99%

Section: Extension With Epistemic Notionsmentioning

confidence: 99%

Section: An Extension With Beliefmentioning

confidence: 99%

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Logics of Responsibility

Abarca¹

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Modeling $$\mathscr {C}^{0}$$ Family Logics for Artificial Intelligence: Doxastic-Temporal Logics for Reasoning About Goals

Oswald,

Rozek,

Ferguson

2024

Künstl Intell

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A Logic-Based Analysis of Responsibility

Abarca

2023

Electron. Proc. Theor. Comput. Sci.

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This paper presents a logic-based framework to analyze responsibility, which I refer to as intentional epistemic act-utilitarian stit theory (IEAUST). To be precise, IEAUST is used to model and syntactically characterize various modes of responsibility, where by 'modes of responsibility' I mean instances of Broersen's three categories of responsibility (causal, informational, and motivational responsibility), cast against the background of particular deontic contexts. IEAUST is obtained by integrating a modal language to express the following components of responsibility on stit models: agency, epistemic notions, intentionality, and different senses of obligation. With such a language, I characterize the components of responsibility using particular formulas. Then, adopting a compositional approach-where complex modalities are built out of more basic ones-these characterizations of the components are used to formalize the aforementioned modes of responsibility. * L ′′ * , so that assumption (⋆⋆) yields that L ′′ * ⊆ |¬φ | m , which contradicts the previously shown fact that L ′′ * ⊆ |φ | m . Thus, M , m, h |= ⊙ S α ϕ → ¬ ⊙ α ¬ϕ for every index m, h , so that ⊙ S α ϕ → ¬ ⊙ α ¬ϕ is indeed valid. It is clear that the rules of inference Modus Ponens, Substitution, and Necessitation for the modal operators all preserve validity.

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A Deontic Stit Logic Based on Beliefs and Expected Utility

Cited by 3 publications

References 30 publications

Logics of Responsibility

Logics of Responsibility

Modeling $$\mathscr {C}^{0}$$ Family Logics for Artificial Intelligence: Doxastic-Temporal Logics for Reasoning About Goals

A Logic-Based Analysis of Responsibility

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