On Logic of Strictly-Deontic Modalities. A Semantic and Tableau Approach

Abstract

Standard deontic logic (SDL) is defined on the basis of possible world semantics and is a logic of alethic-deontic modalities rather than deontic modalities alone. The interpretation of the concepts of obligation and permission comes down exclusively to the logical value that a sentence adopts for the accessible deontic alternatives. Here, we set forth a different approach, this being a logic which additionally takes into consideration whether sentences stand in relation to the normative system or to the system of values under which we predicate the deontic qualifications. By taking this aspect into account, we arrive at a logical system which preserves laws proper to a deontic logic but where the standard paradoxes of deontic logic do not arise. It is a logic of strictly-deontic modalities DR.

Deontic Relationship in the Context of Jan Woleński’s Metaethical Naturalism

“…The above presented semantics constitute a particular combination of the possible-worlds semantics with the relating semantics. The semantics of the latter type were discussed in detail in [9], and its specific cases in [11]. The basis of such semantics is the evaluation of connection, i.e.…”

“…The work by Jarmużek and Klonowski [11] analyses models of relating deontic logic, in which instead of an indexed family of subsets of formulas, an indexed family of binary relations occurring between the formulas was considered. In this case, the unary approach was defined within the binary approach; that is, the family of subsets of formulas indexed by possible worlds was defined by means of the family of binary relations defined on the set of formulas indexed by possible worlds.…”

Modal Boolean Connexive Logics: Semantics and Tableau Approach

“…It is worth to mention that in [5] we introduced a very similar demodalization function. It was in the context of deontic logic while our aim was to underline and preserve the deontic relationships between the sentences related to different changing possible deontic worlds.…”

“…For (D), (T), (4), (B), (5) we have two tableau rules for each: one for the relating relation, one for accessibility Q, in turn:…”

“…So if we want to have a model that satisfies (d), we must close family {R w } w∈W in model M under (d). The same we have to do for the remaining conditions: (Mb1'), (Mb2'), both points of (K), (Du1), (Du2),(D), (T), (4), (B), (5).…”