A Non-Standard Kripke Semantics for the Minimal Deontic Logic

Dyadic Obligations over Complex Actions as Deontic Constraints in the Situation Calculus

Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning ◽

10.24963/kr.2020/26 ◽

2020 ◽

Author(s):

Jens Claßen ◽

James Delgrande

Keyword(s):

Artificial Intelligence ◽

Deontic Logic ◽

Action Theory ◽

Prima Facie ◽

Situation Calculus ◽

Artificial Agents ◽

Planning Techniques ◽

Course Of Action ◽

Reasoning About Action ◽

The Given

With the advent of artificial agents in everyday life, it is important that these agents are guided by social norms and moral guidelines. Notions of obligation, permission, and the like have traditionally been studied in the field of Deontic Logic, where deontic assertions generally refer to what an agent should or should not do; that is they refer to actions. In Artificial Intelligence, the Situation Calculus is (arguably) the best known and most studied formalism for reasoning about action and change. In this paper, we integrate these two areas by incorporating deontic notions into Situation Calculus theories. We do this by considering deontic assertions as constraints, expressed as a set of conditionals, which apply to complex actions expressed as GOLOG programs. These constraints induce a ranking of "ideality" over possible future situations. This ranking in turn is used to guide an agent in its planning deliberation, towards a course of action that adheres best to the deontic constraints. We present a formalization that includes a wide class of (dyadic) deontic assertions, lets us distinguish prima facie from all-things-considered obligations, and particularly addresses contrary-to-duty scenarios. We furthermore present results on compiling the deontic constraints directly into the Situation Calculus action theory, so as to obtain an agent that respects the given norms, but works solely based on the standard reasoning and planning techniques.

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Kripke Semantics for Intersection Formulas

ACM Transactions on Computational Logic ◽

10.1145/3453481 ◽

2021 ◽

Vol 22 (3) ◽

pp. 1-16

Author(s):

Andrej Dudenhefner ◽

Paweł Urzyczyn

Keyword(s):

Kripke Semantics ◽

Type Assignment ◽

Soundness And Completeness

We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system.

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Dynamic Łukasiewicz logic and its application to immune system

Soft Computing ◽

10.1007/s00500-021-05955-3 ◽

2021 ◽

Author(s):

Antonio Di Nola ◽

Revaz Grigolia ◽

Nunu Mitskevich ◽

Gaetano Vitale

Keyword(s):

Immune System ◽

Scalar Multiplication ◽

Kripke Semantics ◽

Łukasiewicz Logic ◽

Lukasiewicz Logic ◽

Regular Algebras

AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$ I D Ł n on the base of n-valued Łukasiewicz logic $${\L }_n$$ Ł n and corresponding to it immune dynamic $$MV_n$$ M V n -algebra ($$IDL_n$$ I D L n -algebra), $$1< n < \omega $$ 1 < n < ω , which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$ ( M , R , ◊ ) that combine the varieties of $$MV_n$$ M V n -algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$ M = ( M , ⊕ , ⊙ , ∼ , 0 , 1 ) and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$ R = ( R , ∪ , ; , ∗ ) into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$ ◊ . Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$ I D Ł n with application in immune system.

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