scholarly journals Expressiveness and Nash Equilibrium in Iterated Boolean Games

2021 ◽  
Vol 22 (2) ◽  
pp. 1-38
Author(s):  
Julian Gutierrez ◽  
Paul Harrenstein ◽  
Giuseppe Perelli ◽  
Michael Wooldridge
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Infinite Sequence ◽  
Multi Agent Systems ◽  
Temporal Logics ◽  
Agent Systems ◽  
Temporal Properties ◽  
Multi Agent ◽  
Game Theoretic ◽  
Boolean Games

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent  has a goal  , represented using (a fragment of) Linear Temporal Logic ( ) . The goal  captures agent  ’s preferences, in the sense that the models of  represent system behaviours that would satisfy  . Each player controls a subset of Boolean variables , and at each round in the game, player is at liberty to choose values for variables in any way that she sees fit. Play continues for an infinite sequence of rounds, and so as players act they collectively trace out a model for , which for every player will either satisfy or fail to satisfy their goal. Players are assumed to act strategically, taking into account the goals of other players, in an attempt to bring about computations satisfying their goal. In this setting, we apply the standard game-theoretic concept of (pure) Nash equilibria. The (possibly empty) set of Nash equilibria of an iterated Boolean game can be understood as inducing a set of computations, each computation representing one way the system could evolve if players chose strategies that together constitute a Nash equilibrium. Such a set of equilibrium computations expresses a temporal property—which may or may not be expressible within a particular fragment. The new notion of expressiveness that we formally define and investigate is then as follows: What temporal properties are characterised by the Nash equilibria of games in which agent goals are expressed in specific fragments of  ? We formally define and investigate this notion of expressiveness for a range of fragments. For example, a very natural question is the following: Suppose we have an iterated Boolean game in which every goal is represented using a particular fragment of : is it then always the case that the equilibria of the game can be characterised within ? We show that this is not true in general.

‘Scene’ as a critical framing device: Extending analysis of chemsex cultures

Sexualities ◽  
2021 ◽  
pp. 136346072199546
Author(s):  
Kerryn Drysdale
Keyword(s):  
Entry Point ◽  
Temporal Logics ◽  
Media Reporting ◽  
Gay Male ◽  
Alternative Approach ◽  
Expert Commentary ◽  
Over Time ◽  
Male Culture

The term ‘chemsex’ references an identifiable set of circumstances and behaviours ascribed to gay male culture at the same time as operating as a politically salient category capable of spurring policy and programmatic responses. Increasingly, the word ‘scene’ is used in association with ‘chemsex’ in media reporting, expert commentary and research on the phenomenon. Rather than dismissing the coupling of chemsex and scene as mere vernacular, ‘scene’ offers a fruitful entry point for exploring how the combination of sex and drugs achieves cultural salience over time. In this article, I read chemsex cultures through the material and representational elements characteristic of ‘scene’. By emphasizing scenes’ temporal logics, I speculate on the value of this alternative approach in generating new understandings of chemsex cultures.

scholarly journals The temporal logic of coalgebras via Galois algebras

2002 ◽  
Vol 12 (6) ◽  
pp. 875-903 ◽  
Author(s):  
BART JACOBS
Keyword(s):  
State Space ◽  
Temporal Logic ◽  
Metric Spaces ◽  
Linear Temporal Logic ◽  
The State ◽  
Temporal Logics ◽  
Computation Tree Logic ◽  
Computation Tree ◽  
Polynomial Functors

This paper introduces a temporal logic for coalgebras. Nexttime and lasttime operators are defined for a coalgebra, acting on predicates on the state space. They give rise to what is called a Galois algebra. Galois algebras form models of temporal logics like Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). The mapping from coalgebras to Galois algebras turns out to be functorial, yielding indexed categorical structures. This construction gives many examples, for coalgebras of polynomial functors on sets. More generally, it will be shown how ‘fuzzy’ predicates on metric spaces, and predicates on presheaves, yield indexed Galois algebras, in basically the same coalgebraic manner.

Deep Reinforcement Learning with Temporal Logics

2020 ◽  
pp. 1-22 ◽  
Author(s):  
Mohammadhosein Hasanbeig ◽  
Daniel Kroening ◽  
Alessandro Abate
Keyword(s):  
Reinforcement Learning ◽  
Temporal Logics
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