25 research outputs found
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
Uniform Strategies
We consider turn-based game arenas for which we investigate uniformity
properties of strategies. These properties involve bundles of plays, that arise
from some semantical motive. Typically, we can represent constraints on allowed
strategies, such as being observation-based. We propose a formal language to
specify uniformity properties and demonstrate its relevance by rephrasing
various known problems from the literature. Note that the ability to correlate
different plays cannot be achieved by any branching-time logic if not equipped
with an additional modality, so-called R in this contribution. We also study an
automated procedure to synthesize strategies subject to a uniformity property,
which strictly extends existing results based on, say standard temporal logics.
We exhibit a generic solution for the synthesis problem provided the bundles of
plays rely on any binary relation definable by a finite state transducer. This
solution yields a non-elementary procedure.Comment: (2012
A characterization of sequential equilibrium in terms of AGM belief revision
In [G. Bonanno, Rational choice and AGM belief revision, Artificial Intelligence, 2009] a semantics for one-stage AGM belief revision was proposed based on choice frames, borrowed from the rational choice literature. In this paper we extend the semantics of choice frames to deal with iterated belief revision and use the corresponding structures to analyze extensive-form games. Choice frames can be used to represent a player's initial beliefs and disposition to change those beliefs when informed that it is her turn to move. If the frame satisfies AGM-consistency and a natural postulate for iterated belief revision, then it is rationalizable by a total pre-order on the set of histories. We show that three properties of this total pre-order, together with the hypothesis of agreement among players, provide a characterization of the notion of consistent assessment, which is the central component of the notion of sequential equilibrium proposed by Kreps and Wilson [Econometrica, 1982].Choice function, AGM belief revision, extensive-form game, sequential equilibrium, iterated belief revision, backward induction.
The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms
The literature specifies extensive-form games in many styles, and eventually
I hope to formally translate games across those styles. Toward that end, this
paper defines , the category of node-and-choice forms. The
category's objects are extensive forms in essentially any style, and the
category's isomorphisms are made to accord with the literature's small handful
of ad hoc style equivalences.
Further, this paper develops two full subcategories: for
forms whose nodes are choice-sequences, and for forms whose
nodes are choice-sets. I show that is "isomorphically enclosed"
in in the sense that each form is isomorphic to
a form. Similarly, I show that is
isomorphically enclosed in in the sense that each
form with no-absentmindedness is isomorphic to a
form. The converses are found to be almost immediate, and the
resulting equivalences unify and simplify two ad hoc style equivalences in
Kline and Luckraz 2016 and Streufert 2019.
Aside from the larger agenda, this paper already makes three practical
contributions. Style equivalences are made easier to derive by [1] a natural
concept of isomorphic invariance and [2] the composability of isomorphic
enclosures. In addition, [3] some new consequences of equivalence are
systematically deduced.Comment: 43 pages, 9 figure
Verification of Agent-Based Artifact Systems
Artifact systems are a novel paradigm for specifying and implementing
business processes described in terms of interacting modules called artifacts.
Artifacts consist of data and lifecycles, accounting respectively for the
relational structure of the artifacts' states and their possible evolutions
over time. In this paper we put forward artifact-centric multi-agent systems, a
novel formalisation of artifact systems in the context of multi-agent systems
operating on them. Differently from the usual process-based models of services,
the semantics we give explicitly accounts for the data structures on which
artifact systems are defined. We study the model checking problem for
artifact-centric multi-agent systems against specifications written in a
quantified version of temporal-epistemic logic expressing the knowledge of the
agents in the exchange. We begin by noting that the problem is undecidable in
general. We then identify two noteworthy restrictions, one syntactical and one
semantical, that enable us to find bisimilar finite abstractions and therefore
reduce the model checking problem to the instance on finite models. Under these
assumptions we show that the model checking problem for these systems is
EXPSPACE-complete. We then introduce artifact-centric programs, compact and
declarative representations of the programs governing both the artifact system
and the agents. We show that, while these in principle generate infinite-state
systems, under natural conditions their verification problem can be solved on
finite abstractions that can be effectively computed from the programs. Finally
we exemplify the theoretical results of the paper through a mainstream
procurement scenario from the artifact systems literature
Reasoning about obligations in Obligationes : a formal approach.
Despite the appearance of `obligation' in their name, medieval obligational dispu-
tations between an Opponent and a Respondent seem to many to be unrelated to
deontic logic. However, given that some of the example disputations found in me-
dieval texts involve Respondent reasoning about his obligations within the context
of the disputation, it is clear that some sort of deontic reasoning is involved. In this
paper, we explain how the reasoning diers from that in ordinary basic deontic logic,
and dene dynamic epistemic semantics within which the medieval obligations can
be expressed and the examples evaluated. Obligations in this framework are history-
based and closely connected to action, thus allowing for comparisons with, e.g., the
knowledge-based obligations of Pacuit, Parikh, and Cogan, and stit-theory. The con-
tributions of this paper are twofold: The introduction of a new type of obligation into
the deontic logic family, and an explanation of the precise deontic concepts involved
in obligationes
Reasoning about Obligations in Obligationes: A Formal Approach
Despite the appearance of `obligation' in their name, medieval obligational dispu- tations between an Opponent and a Respondent seem to many to be unrelated to deontic logic. However, given that some of the example disputations found in me- dieval texts involve Respondent reasoning about his obligations within the context of the disputation, it is clear that some sort of deontic reasoning is involved. In this paper, we explain how the reasoning diers from that in ordinary basic deontic logic, and dene dynamic epistemic semantics within which the medieval obligations can be expressed and the examples evaluated. Obligations in this framework are history- based and closely connected to action, thus allowing for comparisons with, e.g., the knowledge-based obligations of Pacuit, Parikh, and Cogan, and stit-theory. The con- tributions of this paper are twofold: The introduction of a new type of obligation into the deontic logic family, and an explanation of the precise deontic concepts involved in obligationes