From Oughts to Goals: A Logic for Enkrasia

Abstract

This paper focuses on (an interpretation of) the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing 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 multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a nonnormal operator for goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics.

Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

“…In this context, the principle of full communication [14,34,44] roughly says that ϕ can be a piece of group knowledge only if there is some way the agents in G would be able to arrive at the knowledge that ϕ by communicating each of their individual pieces of knowledge. One plausible formal explication of this principle reads: 24 (FC) for all ϕ ∈ L…”

“…. , n}, M, w |= i j (ψ j ∧ ( 1≤j ≤n ψ j → ϕ)) 24 Over monotonic models, the convere of (FC) is always valid; for arbitrary models it may fail. Obvious ways to vary on (FC) concern the language in which the ψ's are contained.…”

“…1 They have been successfully applied to i.a. the dynamics of evidence and beliefs [40], the logic of ability [8,32], conflict-tolerant deontic logic [17], the logical relations between obligations and goals [24], and the analysis of (descriptive or normative) conditionals [9,26]. The generalization from relational semantics to neighbourhood semantics allows one to invalidate certain schemata that are problematic for a given interpretation of the modal operator , but also to include other schemata that would trivialize any normal modal logic.…”

Probabilities with Gaps and Gluts

“…Consistency of premises can be obtained by focusing on maximal consistent subsets, cf. [20,29], or by employing belief revision, as in AGM systems [1]. Mechanisms for dealing with inconsistent information, on the other hand, are developed in a variety of frameworks such as discussive logic [17], adaptive logic [3], Da Costa's logics of formal inconsistency (8,9), relevant logic of [2] and their variants.…”

Probabilities with Gaps and Gluts

“…Consistency of premises can be obtained by focusing on maximal consistent subsets, cf. Rescher and Manor (1970); Klein and Marra (2020), or by employing belief revision, as in AGM systems (Alchourrón et al, 1985). Mechanisms for dealing with inconsistent information, on the other hand, are developed in a variety of frameworks such as discussive logic (Jaskowski, 1948), adaptive logic (Batens, 2001), Da Costa's logics of formal inconsistency (1974; 1989), relevant logic of Anderson and Belnap (1975) and their variants.…”