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We define a family of intuitionistic nonnormal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...) 

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then Xing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multimodal neighborhood logic with three characteristic operators: a nonnormal operator for basic oughts, a nonnormal operator for (...) 

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational normgiving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of settheoretic approach and extended to a twosets model which allows for the separate treatment of obligationnorms and permission norms. The three translation functions connecting the language of deontic logic with the language (...) 

In, a deontic logic is proposed which explicates the idea that a formulaφis obligatory if and only if it is the weakest permission. We give a sound and strongly complete, Hilbert style axiomatization for this logic. As a corollary, it is compact, contradicting earlier claims from Anglbergeret al.. In addition, we prove that our axiomatization is equivalent to Anglberger et al.’s infinitary proof system, and show that our results are robust w.r.t. certain changes in the underlying semantics. 

This paper tackles the problem of inference in normative systems where norms concerning actions and states of affairs appear together. A deontic logic of actions and states is proposed as a solution. It is made up of two independent deontic logics, namely a deontic logic of action and a deontic logic of states, interlinked by bridging definitions. It is shown at a language and a model level how an agent should look for norms to follow in a concrete situation. It (...) 