To download the paper in pdf format click here:  predict.pdf
           If you prefer to download the paper as a postscript file click here:predict.ps

48. Giacomo Bonanno, “Revising predictions ”,  in: Johan van Benthem (ed.), Theoretical aspects of rationality and knowledge
      (TARK 2001), Morgan Kaufman, San Francisco, 2001, pp. 273-286.

Abstract.

    Making a prediction is essentially expressing a belief about the future. It is therefore natural to interpret later predictions as revisions of earlier predictions and to investigate the notion of belief revision in this context. We study, both semantically and syntactically, the following principle of minimum revision of prediction: "as long as there are no surprises, that is, as long as what actually occurs had been predicted to occur, then everything which was predicted in the past, if still possible, should continue to be predicted, and no new predictions should be added". We also study and characterize a notion of consistency of prediction as well as further properties that one might want to impose on the notion of prediction.
 

            To download the paper in pdf format click here: revpred.pdf
           If you prefer to download the paper as a postscript file click here: revpred.ps

49. Giacomo Bonanno, “Branching Time Logic, Perfect Information Games and Backward Induction”,
       Games and Economic Behavior, 36 (1), July 2001, pp. 57-73.
Abstract.
    The logical foundations of game-theoretic solution concepts have so far been developed within the confines of epistemic logic. In this paper we turn to a different branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. We extend the branching time framework by adding agents and by defining the notion of prediction. We show that perfect information games are a special case of extended branching time frames and that the backward-induction solution is a prediction. We also provide a characterization of backward induction in terms of the property of internal consistency of prediction.


           To download the paper in pdf format click here: bi_logic.pdf
           If you prefer to download the paper as a postscript file click here: bi_logic.ps
           Link to the journal article:  published article
 

2002
50. Giacomo Bonanno, Reply to “Social cost and Groves mechanisms”, Economic Notes, 31, 2002, pp. 173-176.

Abstract.

    In my 1992 paper in Economic Notes I argued that the traditional heuristic interpretation of taxes in the pivotal mechanism (in terms of the utility loss imposed by the taxed individual on the rest of society) is not correct, since it takes into account only the effect that the individual has on the decision concerning the project and disregards the effect that the same individual has on the taxes paid by the other members of society. Campbell criticized my observation on the grounds that (1) “[Bonanno’s] analysis cannot be generalized to the case of positive cost because the allocation that [Bonanno] employs to compute social cost is not feasible in that case”, and (2) “[Bonanno’s] definition is not institution free”.  In this paper  I reply to both charges and defend my original observation.

            To download the paper in pdf format click here: Reply.pdf

51. Giacomo Bonanno, “Information, knowledge and belief”, Bulletin of Economic Research, 54, January 2002, pp. 47-67.

Abstract.

    We model information as possibilities consistent with signals received from the environment. Knowledge is obtained by reasoning about the signals received as well as those that might have been received but were not. We use the term `knowledge' to refer to those beliefs that are obtained by reasoning about the available information and nothing else. That is, one ought to be able to fully justify what one knows by means of the information that is available to her. We use the term `belief' to refer to those beliefs that are based on information but not necessarily only on information. We investigate the relationship between information, knowledge and belief, as well as the issue of updating knowledge and belief in response to changes in information.

            To download the paper in pdf format click here: information.pdf
           If you prefer to download the paper as a postscript file click here:information.ps

52. Giacomo Bonanno, “Modal logic and game theory: two alternative approaches”, Risk Decision and Policy, 7,
                                         December 2002, pp. 309-324.

Abstract.

    Two views of game theory are discussed: (1) game theory as a description of the behavior of rational individuals who recognize each other's rationality and reasoning abilities, and (2) game theory as an internally consistent recommendation to individuals on how to act in interactive situations. It is shown that the same mathematical tool, namely modal logic, can be used to explicitly model both views.

            To download the paper in pdf format click here: Rimini.pdf
           If you prefer to download the paper as a postscript file click here: Rimini.ps

2003

53. Giacomo Bonanno, “A syntactic characterization of perfect recall in extensive games”, Research in Economics,
                                         57 (3), September 2003, pp. 201-217.

Abstract.

    We provide a syntactic characterization of the property of perfect recall in extensive games. The language we use is basic temporal logic with the addition of a knowledge operator for every player.
.

            To download the paper in pdf format click here: Loft5.pdf
           If you prefer to download the paper as a postscript file click here: Loft5.ps
           Link to the journal article:  http://authors.elsevier.com/sd/article/S1090944303000358
 

54. Giacomo Bonanno, “Memory of past beliefs and actions”, Studia Logica, 75 (1), October 2003, pp. 7-30.

Abstract.

    Two notions of memory are studied both syntactically and semantically: memory of past beliefs and memory of past actions. The analysis is carried
out in a basic temporal logic framework enriched with beliefs and actions.
.

            To download the paper in pdf format click here: Memory.pdf
           If you prefer to download the paper as a postscript file click here: Memory.ps
           Link to the journal article:  http://ipsapp009.kluweronline.com/IPS/frames/toc.aspx?J=5187&I=51#

2004

 

55. Giacomo Bonanno, “Memory and perfect recall in extensive games”, Games and Economic Behavior, 47 (2), May 2004, pp. 237-256.

Abstract.

    The notion of perfect recall in extensive games was introduced by Kuhn (1953), who interpreted it as "equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves''. We provide a characterization and axiomatization of perfect recall based on two notions of memory: (1) memory of past knowledge and (2) memory of past actions..
.

            To download the paper in pdf format click here: PerfRec.pdf
           Also available at:  http://repositories.cdlib.org/postprints/26
            Link to the journal article:  http://authors.elsevier.com/sd/article/S0899825603001933

56. Giacomo Bonanno, “A characterization of von Neumann games in terms of memory", Synthese, 139 (2), March 2004, pp. 237-256 (and Knowledge, Rationality and Action, 2004, pp. 117-131).

Abstract.

    An information completion of an extensive game is obtained by extending the information partition of every player from the set of her decision nodes to the set of all
nodes. The extended partition satisfies Memory of Past Knowledge (MPK) if at any node a player remembers what she knew at earlier nodes. It is shown that MPK can be satisfied
in a game if and only if the game is von Neumann (vN) and satisfies memory at decision nodes (the restriction of MPK to a player’s own decision nodes). A game is vN if any two
decision nodes that belong to the same information set of a player have the same number of predecessors. By providing an axiom for MPK we also obtain a syntactic characterization
of the said class of vN games..
.

            To download the paper in pdf format click here: vNM.pdf
           Also available at:  http://repositories.cdlib.org/postprints/24
            Link to the journal article: http://journals.kluweronline.com/article.asp?PIPS=5256223orhttp://dx.doi.org/10.1023/B:SYNT.0000024905.25386.3d

2005

57. Giacomo Bonanno, “A simple modal logic for belief revision”, Synthese, 147 (2), 2005, pp. 193-228 (and Knowledge, Rationality and Action, 2005, pp. 5-40).
      Reprinted in van der Hoek, Wiebe, (Ed.), Uncertainty, rationality and agency, Springer, Dordrect, 2006, pp. 139-174.

Abstract.

    We propose a modal logic based on three operators, representing intial beliefs, information and revised beliefs. Three simple axioms are used to provide a sound and complete
axiomatization of the qualitative part of Bayes' rule. Some theorems of this logic are derived concerning the interaction between current beliefs and future beliefs. Information flows
and iterated revision are also discussed.
.

            To download the paper in pdf format click here: BelRev.pdf
            Link to the journal article: http://dx.doi.org/10.1007/s11229-005-1348-8

2006

58. Giacomo Bonanno, “Belief revision in a temporal framework: extended abstract”, Proceedings of the 7th conference on Logic and the Foundations of Game and Decision Theory, University of Liverpool, 2006, pp. 43-50.
Abstract.

    The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update. The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on belief revision and propose a temporal framework that allows for iterated revision. We model the notion of "minimal" or "conservative" belief revision by considering logics of increasing strength. We move from one logic to the next by adding one or more axioms and show that the corresponding logic captures more stringent notions of minimal belief revision.

            To download the paper in pdf format click here: LOFT7.pdf
 


2007

59. Giacomo Bonanno, “Axiomatic characterization of the AGM theory of belief revision in a temporal logic”, Artificial Intelligence,  171 (2-3), February 2007, pp. 144–160.

Abstract.

    Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger,l ogic provides an axiomatic characterization of the full set of AGM postulates.

            To download the pre-print version in pdf format click here: AGM.pdf

            Link to the journal article: http://dx.doi.org/10.1016/j.artint.2006.12.001


60. Giacomo Bonanno, "Temporal interaction of information and belief", Studia Logica,  86, 2007, pp. 381-407.

Abstract.

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided.

           To download the paper in pdf format click here: InfBel.pdf


2008

61. Giacomo Bonanno, "A syntactic approach to rationality in games with ordinal payoffs", in: G. Bonanno, W. van der Hoek and M. Wooldridge (eds.), Logic and the Foundations of Game and Decision Theory, Texts in Logic and Games Series, Amsterdam University Press, 2008, pp. 59-86.  (ISBN: 978 908 964 0260)

Abstract.

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994). Frame characterization results are also provided.

           To download the paper in pdf format click here: CBR.pdf


62. Giacomo Bonanno, “Belief revision in a temporal framework”, in Krzysztof R. Apt and Robert van Rooij (eds.), New Perspectives on Games and Interaction, Texts in Logic and Games Series, Amsterdam University Press, 2008, pp. 45-79.

Abstract.

We study a branching-time temporal logic of belief revision where the interaction of belief and information is modeled explicitly. The logic is based on three modal operators: a belief operator, an information operator and a next-time operator. We consider three logics of increasing strength. The first captures the most basic notion of minimal belief revision. The second characterizes the qualitative content of Bayes' rule. The third is the logic proposed in Bonanno, Artificial Intelligence, 2007, where some aspects of its relationship with the AGM theory of belief revision were investigated. We further explore the relationship to AGM with the help of semantic structures that have been used in the rational choice literature. Further strengthening of the logic are also investigated.

           To download the paper in pdf format click here: KNAW.pdf


63. Giacomo Bonanno, "A sound and complete temporal logic for belief revision", in Cédric Dégremont, Laurent Keiff and Helge Rückert (eds), Dialogues, Logics and Other Strange Things: Essays in Honour of Shahid Rahman, College Publications, 2008 (http://www.collegepublications.co.uk/tributes/?00007), pp. 67-80.

Abstract.

Branching-time temporal logic offers a natural setting for a theory of belief change. We propose a temporal logic that, besides the next-time operator, contains a belief operator and an information operator. It is shown that this logic is sound and complete with respect to the class of branching-time frames augmented, for each instant t, with a set of states and two binary relations on it, representing beliefs and information, respectively.

           To download the paper in pdf format click here: Complete.pdf
 


2009

64. Giacomo Bonanno, "Rational choice and AGM belief revision", Artificial Intelligence, 173, 2009, pp. 1194-1203.

Abstract.

We establish a correspondence between the rationalizability of choice studied in the revealed preference literature and the notion of minimal belief revision captured by the AGM postulates. A choice frame consists of a set of alternatives W, a collection C of subsets of W (representing possible choice sets) and a function f  from C  into the set of subsets of W  (representing choices made). A choice frame is rationalizable if there exists a total pre-order R on W such that, for every E in C, f(E) coincides with the best elements of E relative to R. We re-interpret choice structures in terms of belief revision. An interpretation is obtained by adding a valuation that assigns to every atom p the subset of W at which p is true. Associated with an interpretation is an initial belief set and a partial belief revision function. A choice frame is AGM-consistent if, for every interpretation of it, the associated partial belief revision function can be extended to a full-domain belief revision function that satisfies the AGM postulates. It is shown that a finite choice structure is AGM-consistent if and only if  it is rationalizable..

           To download the pre-print version  in pdf format click here: Choice_AI.pdf

           Link to the journal article: http://dx.doi.org/10.1016/j.artint.2009.05.001
 
 
 
 

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