Action Logic (Deontic)

Origin. Segerberg (1980s), Belnap and Perloff (1988). Agency in deontic logic. stit (sees to it that). Actions as logical objects. Foundation for agent responsibility.

Models. Branching time with agents. Choice functions. Agent ensures outcome across choices. Deliberative vs causal agency.

Formalism.

stit operator: [i stit: φ]: agent i sees to it that φ. i's choice guarantees φ.

Branching time: Tree structure. Moments and histories. Choices partition histories at moments.

Achievement stit: [i astit: φ]: i acts so φ, alternative had ¬φ. Counterfactual contrast.

Deliberative stit: [i dstit: φ]: i ensures φ, could have done otherwise. Free will assumption.

Ought-to-do: O[i stit: φ]: i ought to see to φ. Deontic on actions.

Ability: Can(i, φ): some choice of i guarantees φ. ◇[i stit: φ]

Group agency: [G stit: φ]: group G jointly ensures φ. Coalition choices.

Independence: Agent choices independent. Product of individual choices.

STIT semantics: w, m/h ⊨ [i stit: φ] iff ∀h' ∈ Choice_i(m): w, m/h' ⊨ φ Agent's choice cell satisfies φ.

Symbols.

Symbol	Unicode	Name	Meaning
stit	—	Sees to it	Agency
Choice_i	—	Choices	Agent's options
m/h	—	Moment/history	Index
O	—	Ought	Obligation

Metatheory. Branching-time semantics. Axiomatization exists. Decidable fragments. Complexity varies.

Applies to. Legal responsibility. Moral philosophy. Agent theory. Robot ethics. Causation.

Limitations. Complex semantics. Idealized agency. Infinite branching. Determinism/freedom debate.