Информационная система "Конференции"

Abstracts

Non-classical logics, proof theory and universal algebra

The report concerns a new version of propostional deontic logic (PDL) language and an original treatment of its semantics, both invented by the author of the report and unexplored in existing literature.

The considered variation of the PDL language formalizes a particular version of the philosophical theory of operative individual intentions rooted in some works of professor V. O. Lobovikov and of the report’s author. Thus all the deontic propositional formulas characterize the operative intentions of a singular and the same agent who is not described any further. These intentions are represented by terms of a specific kind.

PDL formulas are build from these terms with the aid of propositional connectives and three operators creating atomic formulas, namely the O-operator (obligation), P-operator (permission) and <…>-operator (developing of intention by the agent). Hence the proposed notion of a PDL-formula turns out to be rather restrictive as it does not allow iteration of deontic operators.

The most specific feature of the deontic logic semantics under consideration is that it does involve neither any kind of Kripke-type possible-world structures nor any use of many-valued logic constructions. Rather, it is built on a basis of a single possible world description supplied with a special kind of relation on the set of terms.

The described approach to deontic logic semantics opens a possibility of defining dyadic deontic modalities in terms of monadic ones. The main subject of the report is the discussion of the conditions of adequacy of such definition. The report will also cover some questions concerning representation and treatment of the famous “paradoxical” formulas of standard deontic logic in the framework of the proposed new PDL language and its semantics, such as “Ross paradox”, “paradoxes of derived obligation” and others.

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