scholarly journals OBLIGATION, FREE CHOICE, AND THE LOGIC OF WEAKEST PERMISSIONS

2015 ◽  
Vol 8 (4) ◽  
pp. 807-827 ◽  
Author(s):  
ALBERT J.J. ANGLBERGER ◽  
NOBERT GRATZL ◽  
OLIVIER ROY

AbstractWe introduce a new understanding of deontic modals that we callobligations as weakest permissions. We argue for its philosophical plausibility, study its expressive power in neighborhood models, provide a complete Hilbert-style axiom system for it and show that it can be extended and applied to practical norms in decision and game theory.

1996 ◽  
Vol 26 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Joseph Heath

Recent developments in game theory have shown that the mathematical models of action so widely admired in the study of economics are in fact only particular instantiations of a more general theoretical framework. In the same way that Aristotelian logic was ‘translated’ into the more general and expressive language of predicate logic, the basic action theoretic underpinnings of modern economics have now been articulated within the more comprehensive language of game theory. But precisely because of its greater generality and expressive power, game theory has again revived the temptation to apply formal models of action to every domain of social life. This movement has been fuelled by some notable successes. Game theory has provided useful insights into the logic of collective action in the theory of public goods, and strategic models of voting have illustrated important aspects of institutional decision-making. But this extension of formal models into every area of social interaction has also encountered significant difficulties, despite the fact that contemporary decision theory has weakened its basic assumptions to the point where it teeters constantly on the brink of vacuity.


2019 ◽  
Vol 12 (4) ◽  
pp. 702-735
Author(s):  
TAI-WEI HU ◽  
MAMORU KANEKO ◽  
NOBU-YUKI SUZUKI

AbstractWe develop a series of small infinitary epistemic logics to study deductive inference involving intra-/interpersonal beliefs/knowledge such as common knowledge, common beliefs, and infinite regress of beliefs. Specifically, propositional epistemic logics GL (Lα) are presented for ordinal α up to a given αo (αo ≥ ω) so that GL(L0) is finitary KDn with n agents and GL(Lα) (α ≥ 1) allows conjunctions of certain countably infinite formulae. GL(Lα) is small in that the language is countable and can be constructive. The set of formulae Lα is increasing up to α = ω but stops at ω We present Kripke-completeness for GL(Lα) for each α ≤ ω, which is proved using the Rasiowa–Sikorski lemma and Tanaka–Ono lemma. GL(Lα) has a sufficient expressive power to discuss intra-/interpersonal beliefs with infinite lengths. As applications, we discuss the explicit definability of Axioms T (truthfulness), 4 (positive introspection), 5 (negative introspection), and of common knowledge in GL(Lα) Also, we discuss the rationalizability concept in game theory in our framework. We evaluate where these discussions are done in the series GL(Lα), α ≤ ω.


2019 ◽  
Vol 27 (4) ◽  
pp. 387-410 ◽  
Author(s):  
Federico L G Faroldi

Abstract In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis (that deontic modals are not hyperintensional) leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power (e.g. Ross’s paradox, the Gentle Murderer, The Good Samaritan, Free Choice Permission and the Miners’ Paradox disappear). I then propose a philosophical analysis of this thesis and outline some consequences. In Section 1 I introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics.


2016 ◽  
Vol 26 ◽  
pp. 325 ◽  
Author(s):  
William Starr

This paper proposes a semantics for free choice permission that explains both the non-classical behavior of modals and disjunction in sentences used to grant permission, and their classical behavior under negation. It also explains why permissions can expire when new information comes in and why free choice arises even when modals scope under disjunction. On the proposed approach, deontic modals update preference orderings, and connectives operate on these updates rather than propositions. The success of this approach stems from its capacity to capture the difference between expressing the preferences that give rise to permissions and conveying propositions about those preferences. 


Author(s):  
Ein-Ya Gura ◽  
Michael Maschler
Keyword(s):  

Author(s):  
Zhu Han ◽  
Dusit Niyato ◽  
Walid Saad ◽  
Tamer Basar ◽  
Are Hjorungnes

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