Connecting Logics of Choice and Change

Abstract

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.

Stit Logics, Games, Knowledge, and Freedom

“…6 We refer to i as the anti-group of i-the group including all agents except i. R4 then states that each choice of i's anti-group at w is equal to the intersection of the choices of its members at w. 7 In what follows, we will confine ourselves to CKF + 's, which will make the comparison with strategic games easier. 8 To illustrate, Figure 1 exemplifies a CKF + : [w] 1 [w ] 1 6 In case this condition seems to strong, it is helpful to think of one the agents as "nature," which removes any remaining indeterminacy once all the more ordinary agents have made their choices; this tactic was mentioned in [24, p. 91]. 7 R4 is just an instance of the game-theoretical principle of additivity, which characterizes the construction of all groups in group STIT; see section 5 below.…”

“…7 R4 is just an instance of the game-theoretical principle of additivity, which characterizes the construction of all groups in group STIT; see section 5 below. 8 Actually, the correspondence between games and consequentialist CKF + (see below for a definition) can also be established without imposing condition R3; see, for example, van Benthem and Pacuit [8] and Tamminga [27]. However, the condition makes the proof of such a correspondence much more straightforward and general.…”

“…Approaching some phenomena of game theory without imposing independence is clearly possible and equally sound. For instance, van Benthem and Pacuit [8] suggests dropping the totality of the outcome function o in order to model the game-theoretical notion of a correlation, where there is some form of dependence between some agent's choices. This suggestion is in line with a general tradition of Dynamic Logics in modeling game-theoretical notions.…”

“…The logic was later enriched with a notion of "freedom" that deserves attention, since it is thought to capture the margin of action that a combined choice of all the other agents leaves to a particular agent i. Van Benthem and Pacuit [8] contains a very interesting comparison between STIT and MGL, and proves that there is an embedding of the former into the latter. Here, we continue the comparison with a mutual embedding between MGL's operator for ex interim knowledge-e.i.-knowledge, for short-and the Chellas stit.…”

“…First, we try to clarify potential of STIT as a logical foundation for game theory by describing its adequacy for modeling certain game-theoretic notions. And second, we compare STIT with Matrix Game Logic, Dynamic Logic first introduced by van Benthem in [5] and developed in his later [6] and [7]; in this comparitive project, we continue, and hope to advance, the conversation initiated by van Benthem and Pacuit [8]. 3 The chapter proceeds as follows.…”