Alternative Axiomatics and Complexity of Deliberative Stit Theories

Balbiani, Philippe; Herzig, Andreas; Troquard, Nicolas

doi:10.1007/s10992-007-9078-7

Cited by 56 publications

(66 citation statements)

References 9 publications

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“…What follows here has strong resemblances to earlier work by a number of authors, including (Herzig and Lorini 2010;Balbiani et al 2008;Lorini 2010;Lorini et al 2009). 13 One can also have more abstract worlds in so-called 'models of games', as is usual in epistemic game theory, see (Aumann 1999)-but this generality is not needed in what follows.…”

Section: Modal Logic Of Matrix Gamessupporting

confidence: 81%

“…We will be very brief, only touching on the key notions we need later in this chapter. For more information, the reader is invited to consult (Horty 2001;Belnap et al 2001;Horty and Belnap 1995;Balbiani et al 2008).…”

Section: Preliminaries: the Stit Frameworkmentioning

confidence: 99%

“…However, there is also the issue of syntactic proof rules for reasoning about action. The following axiomatization was proven sound and complete for the class of all STIT models in (Xu 1995;Balbiani et al 2008):…”

Section: Stit Semanticsmentioning

confidence: 99%

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Connecting Logics of Choice and Change

Benthem

Pacuit

2014

Outstanding Contributions to Logic

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This chapter is an attempt at clarifying the current scene of sometimes competing action logics, looking for compatibilities and convergences. Current paradigms for deliberate action fall into two broad families: dynamic logics of events, and STIT logics of achieving specified effects. We compare the two frameworks, and show how they can be related technically by embedding basic STIT into a modal logic of matrix games. Amongst various things, this analysis shows how the attractive principle of independence of agents' actions in STIT might actually be a source of high complexity in the total action logic. Our main point, however, is the compatibility of dynamic logics with explicit events and STIT logics based on a notion that we call 'control'-and we present a new system of dynamic-epistemic logic with control that has both. Finally, we discuss how dynamic logic and STIT face similar issues when including further crucial aspects of agency such as knowledge, preference, strategic behavior, and explicit acts of choice and deliberation.

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Section: Modal Logic Of Matrix Gamessupporting

confidence: 81%

Section: Preliminaries: the Stit Frameworkmentioning

confidence: 99%

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Connecting Logics of Choice and Change

Benthem

Pacuit

2014

Outstanding Contributions to Logic

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“…These are exactly the abstract models of the deliberative stit discussed in (Balbiani et al 2008) except that there the models have a slightly different, but equivalent, form because they incorporate an extra, very strong 'independence of agents' assumption characteristic of stit.…”

Section: Languagementioning

confidence: 99%

Some Examples Formulated in a ‘Seeing to It That’ Logic: Illustrations, Observations, Problems

Sergot

2014

Outstanding Contributions to Logic

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The chapter presents a series of small examples and discusses how they might be formulated in a 'seeing to it that' logic. The aim is to identify some of the strengths and weaknesses of this approach to the treatment of action. The examples have a very simple temporal structure. An element of indeterminism is introduced by uncertainty in the environment and by the actions of other agents. The formalism chosen combines a logic of agency with a transition-based account of action: the semantical framework is a labelled transition system extended with a component that picks out the contribution of a particular agent in a given transition. Although this is not a species of the stit logics associated with Nuel Belnap and colleagues, it does have many features in common. Most of the points that arise apply equally to stit logics. They are, in summary: whether explicit names for actions can be avoided, the need for weaker forms of responsibility or 'bringing it about' than are captured by stit and similar logics, some common patterns in which one agent's actions constrain or determine the actions of another, and some comments on the effects that level of detail, or 'granularity', of a representation can have on the properties we wish to examine.

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“…17), viz. the (atemporal and individual version of) Ldm, as well as its simplification proposed in (Balbiani et al, 2008b). For historical reasons, Ldm is sometimes referred to as the logic of Chellas STIT.…”

Section: Background: Xu's Logic Ldmmentioning

confidence: 99%