In this paper, I will discuss boulesic and deontic logic and the relationship between these branches of logic. By ‘boulesic logic,’ or ‘the logic of the will,’ I mean a new kind of logic that deals with ‘boulesic’ concepts, expressions, sentences, arguments and systems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be the case that’ and ‘individual x accepts that it is the case that.’ These expressions will be symbolised by two sentential operators that take individuals and sentences as arguments and give sentences as values. Deontic logic is a relatively well-established branch of logic. It deals with normative concepts, sentences, arguments and systems. In this paper, I will show how deontic logic can be grounded in boulesic logic. I will develop a set of semantic tableau systems that include boulesic and alethic operators, possibilist quantifiers and the identity predicate; I will then show how these systems can be augmented by a set of deontic operators. I use a kind of possible world semantics to explain the intended meaning of our formal systems. Intuitively, we can think of our semantics as a description of the structure of a perfectly rational will. I mention some interesting theorems that can be proved in our systems, including some versions of the so-called hypothetical imperative. Finally, I show that all systems that are described in this paper are sound and complete with respect to their semantics.
In this paper, we present Carnap’s modal logic C, which is one of the first attempts to use the concept of possible world (that of state description in the Carnapian original terminology) in shaping the semantics for modalities. Some older technical results, which concern the logic C, are summarized, namely two different kinds of axiomatization of C, one unusual characterization of C as the only set of formulae having one special property, and semantical and syntactical relations of C to S5. The fact that C is not closed under the universal substitution is shortly discussed. Finally, the predicate version of C, which is not axiomatizable, is defined., V tomto příspěvku prezentujeme Carnapovu modální logiku C, která je jedním z prvních pokusů o využití konceptu možného světa (státního popisu v karnapské původní terminologii) při formování sémantiky modalit. Jsou shrnuty některé starší technické výsledky, které se týkají logiky C, a to dva různé druhy axiomatizace C, jedna neobvyklá charakterizace C jako jediná množina vzorců s jednou speciální vlastností a sémantické a syntaktické vztahy C až S5. Krátce je diskutována skutečnost, že C není uzavřena pod univerzální substitucí. Nakonec je definována predikátová verze C, která není axiomatizovatelná., and Vít Punčochář