A Stit Logic of Intentionality

Abarca, Aldo Iván Ramírez; Broersen, Jan

doi:10.1007/978-3-031-26622-5_8

Cited by 2 publications

(9 citation statements)

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“…For α ∈ Ags, the equivalence relation ∼ α is the usual indistinguishability relation, borrowed from epistemic logic, that represents α's uncertainty: whatever holds at all epistemically accessible indices is what an agent knows. As for the function τ, it assigns to each agent the topology of intentions, according to the ideas presented by [3]. The open sets of any such topology are taken to be p-d intentions for bringing about circumstances.…”

Section: Choice Satisfies Two Constraints: (Nc) No Choice Between Und...mentioning

confidence: 99%

“…α is then defined by the following rule: for 3 Just as in the case of objective ought-to-do's, this ordering allows us to define a subjectively optimal set of actions…”

Section: Choice Satisfies Two Constraints: (Nc) No Choice Between Und...mentioning

confidence: 99%

“…• (Rules of inference) Modus Ponens, Substitution, and Necessitation for all modal operators. For a discussion of all these axioms and schemas, the reader is referred to [1,18,3]. An important result for Λ R , then, is the following proposition, whose proof is relegated to Appendix A.…”

Section: Axiomatizationmentioning

confidence: 99%

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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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Section: Choice Satisfies Two Constraints: (Nc) No Choice Between Und...mentioning

confidence: 99%

“…α is then defined by the following rule: for 3 Just as in the case of objective ought-to-do's, this ordering allows us to define a subjectively optimal set of actions…”

Section: Choice Satisfies Two Constraints: (Nc) No Choice Between Und...mentioning

confidence: 99%

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A Logic-Based Analysis of Responsibility

Abarca

2023

Electron. Proc. Theor. Comput. Sci.

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“…Although the extension of IEAUST with p-1 belief and with doxastic oughtto-do's has already been presented in my joint work with Jan Broersen (Abarca & Broersen, 2022), a full-fledged exploration of the logic in the context of responsibility attribution-as well as an exploration of its metalogic results-remains to be done.…”

Section: Appendix C Metalogic Results For Eaustmentioning

confidence: 99%

“…-Chapter 6 is an elaboration of a framework that was presented in an extended abstract developed with Jan Broersen (Abarca & Broersen, 2022).…”

Section: Sources Of the Original Materialsmentioning

confidence: 99%

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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A Stit Logic of Intentionality

Cited by 2 publications

References 18 publications

A Logic-Based Analysis of Responsibility

A Logic-Based Analysis of Responsibility

Logics of Responsibility

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