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Deontic Logics as Axiomatic Extensions of First-Order Predicate Logic: An Approach Inspired by Wolniewicz’s Formal Ontology of Situations

Foundation for Computer Science, Logic and Formalized Mathematics, Warsaw, Poland
Axioms 2019, 8(4), 109; https://doi.org/10.3390/axioms8040109
Received: 14 August 2019 / Revised: 30 September 2019 / Accepted: 1 October 2019 / Published: 6 October 2019
(This article belongs to the Special Issue Deductive Systems)
The aim of this article is to present a method of creating deontic logics as axiomatic theories built on first-order predicate logic with identity. In the article, these theories are constructed as theories of legal events or as theories of acts. Legal events are understood as sequences (strings) of elementary situations in Wolniewicz′s sense. On the other hand, acts are understood as two-element legal events: the first element of a sequence is a choice situation (a situation that will be changed by an act), and the second element of this sequence is a chosen situation (a situation that arises as a result of that act). In this approach, legal rules (i.e., orders, bans, permits) are treated as sets of legal events. The article presents four deontic systems for legal events: AEP, AEPF, AEPOF, AEPOFI. In the first system, all legal events are permitted; in the second, they are permitted or forbidden; in the third, they are permitted, ordered or forbidden; and in the fourth, they are permitted, ordered, forbidden or irrelevant. Then, we present a deontic logic for acts (AAPOF), in which every act is permitted, ordered or forbidden. The theorems of this logic reflect deontic relations between acts as well as between acts and their parts. The direct inspiration to develop the approach presented in the article was the book Ontology of Situations by Boguslaw Wolniewicz, and indirectly, Wittgenstein’s Tractatus Logico-Philosophicus.
Keywords: deontic logic; ontology of situations; semantics of law; formal theory of law; Wittgenstein; Wolniewicz deontic logic; ontology of situations; semantics of law; formal theory of law; Wittgenstein; Wolniewicz
MDPI and ACS Style

Malec, A. Deontic Logics as Axiomatic Extensions of First-Order Predicate Logic: An Approach Inspired by Wolniewicz’s Formal Ontology of Situations. Axioms 2019, 8, 109.

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