For very recent, or unpublished, papers please go to

1. "Towards a Theory of Social Software" (preliminary version). Presented at Deon'02, Imperial College, London, England.
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2. "States of Knowledge." To be presented at WOLLIC-2002, Rio di Janeiro, Brazil.
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3. "Finite information logic" (research report) (with Jouko Vaananen). Presented at Clifford-2002, Tulane University, New Orleans, Louisiana.
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4. "A Knowledge-Based Semantics of Messages" (with R. Ramanujam).
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5. "States of Knowledge and Group Action."
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6. "Finite Information Logic" (with Jouko Vaananen).
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7. "Some Results on Adjusted Winner" (with Eric Pacuit and Samer Salame).
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8. "Probabilistic Conditionals Are Almost Monotonic" (with Matthew Johnson)
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9. "Sentences, Propositions and Logical Omniscience, or What does Deduction tell us?"
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10. "D-Structures and their semantics"
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11. "Levels of Knowledge, Games, and Group Action"
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12. "Logical Omniscience in the Many Agent Case"
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13. "Beliefs, Belief Revision, and Splitting Languages"
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14. "Knowledge and the Problem OF Logical Omniscience"
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15. "On the Interaction between Computer Science and Economics" with Eric Pacuit
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16. "A Knowledge based semantics of messages"
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17. "Social Software"
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18. "Is There a Logic of Society"
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19. "On Public Language and Private Language"
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(This is a partial list of some of the post-1990 papers.)



1. "Communication, Consensus and Knowledge," (with P. Krasucki), J. Economic Theory 52 (1990), pp. 178-189.

A connection between knowledge as studied in mathematical economics and in distributed computing.

2. "Levels of knowledge in distributed computing," (with P. Krasucki), Sadhana - Proc. Ind. Acad. Sci. 17 (1992), pp. 167-191.

We show a correspondence between levels of knowledge, with common knowledge being the highest level, and certain regular languages.

3. "Probabilistic Knowledge and Probabilistic Common Knowledge," (with Paul Krasucki and Gilbert Ndjatou), ISMIS 90, North Holland (1990), pp. 1-8.

We show how to answer questions like "How much does A know about B's knowledge of C?", in a manner which naturally generalises Shannon's definition. In particular we show how there can be probabilistic common knowledge in a group even when there is no common knowledge in the usual sense.

4. "Finite and Infinite Dialogues", in the Proceedings of a Workshop on Logic from Computer Science, Ed. Moschovakis, MSRI publications, Springer 1991, pp. 481-498.

There are various puzzles current in the literature, the muddy children puzzle for instance, which nicely bring out the structure of common knowledge and the role it plays in communication. We consider variants and extensions of this puzzle including some where a conversation may go on through the transfinite ordinals before terminating and a game theoretic version where one may speak even when one is not sure but can be penalized for an incorrect answer.

5. "Monotonic and Non-monotonic Logics of Knowledge", in Fundamenta Informatica special issue, Logics for Artificial Intelligence vol XV (1991), pp. 255-274.

Shows how to interpret a non-monotonic rule of McCarthy and obtains completeness and decidability results. The intuition is that if some A is all that someone knows, then we can reason non-monotonically about that person's state of knowledge. The Mr. Sum and Mr. Product puzzle can be understood in such a framework. An earlier version of this paper appeared in FST-TCS, (1984)

6. "A Test for Fuzzy Logic", SIGACT NEWS, 22, 3, Summer 1991, pp. 49-50.

Examines the question of whether Fuzzy logic can provide an adequate semantics for our linguistic practices. It is argued that Zadeh's fuzzy values do not have a basis on reality, even though they do seem to capture some intuition. Some experimental results are reported.

7. "A Logical Study of Distributed Transition Systems," with Lodaya, Ramanujam and Thiagarajan. Information and Computation 119, May 1995, pp. 91-119.

A study of a variety of logics for reasoning about concurrency.

8. "Notes of Rohit Parikh's lectures on Reasoning about Knowledge," by Anna Maria Zanaboni. (The lectures were given in Acireale at an International School for Computer Scientists) published in Italy, summer 1993. (Cassa di Risparmio di Padova e Rovigo)

9. "Vagueness and Utility: the Semantics of Common Nouns," in Linguistics and Philosophy 17 (1994), pp. 521-35.

We point out that to date there do not exist satisfactory logics or semantics for vague predicates. We show that these predicates are person dependent, i.e. the way they are applied varies from person to person and also from occasion to occasion. Hence a theory is needed of why they are useful in communication and do not lead to difficulties. We show how there are settings where despite some differences in application by the various individuals involved, communication is useful. These are the (robust) settings in which we do in fact use these predicates, avoiding them in other areas where such sturdiness does not obtain.

10. "Logical omniscience," in Logic and Computational Complexity, Ed. Leivant, Springer Lecture Notes in Computer Science no. 960, (1995) 22-29.
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Current logics of knowledge have the property that under their definition of what it means for $i$ to know some formula A, $i$ knows all valid formulas and also the consequences of anything that $i$ knows. This is implausible and to find more plausible definitions of knowledge is the problem of logical omniscience. We make some algorithim based suggestions. An earlier version of this paper appeared in ISMIS 1987, ed. Z. Ras, pp. 432-439.

12. "Language as social software" (abstract) International Congress on Logic, Methodology and Philosophy of Science (1995), page 417. Full version to appear in Future Pasts, Ed. Floyd and Shieh, Oxford U. Press, 2000.
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One can view language as playing the role of a system of signals to facilitate social behaviour. It turns out that this view is very flexible and can explain various philosophical puzzles like Searle's Chinese room puzzle or Quine's indetermincy of translation thesis.

13. "Knowledge based computation" (Extended abstract), in Proceedings of AMAST-95, Montreal, July 1995, Edited by Alagar and Nivat, LNCS no. 936, pp. 127-42.

A short survey of work in this area done to date.

14. "Topological Reasoning and The Logic of Knowledge" (with Dabrowski and Moss), Annals of Pure and Applied Logic 78 (1996), pp. 73-110.

It was noticed long ago by Goedel and Tarski that topological spaces can be used to analyse modal notions. We carry the ball in the opposite direction and show that many topological notions have a strong modal-theoretical and knowledge-theoretic character and that a modal intuition underlies some of our reasoning about topology. While it is true that one's knowledge depends on one's evidence, traditional definitions of knowledge leave out the fact that one can gather or improve one's knowledge. E.g. a measurement of some quantity can be made more accurate by using better instruments. This observation allows us to develop a logic with two modalities, one for knowledge and the other for effort. Some topological notions like closed or {\em perfect can be defined in this logic. We provide axiomatizations and prove completeness results.

15. "How far can we formalize language games?" in The Foundational Debate, edited by DePauli-Scimanovich, Koehler and Stadler, Kluwer Academic (1995) pp. 89-100.

Wittgenstein's views in the Philosophy of Mathematics are examined and shown to be very modern in spirit. We raise the question how far one can provide formal versions of language games as a way of making certain problems more explicit.

16. "Vague predicates and language games," Theoria Spain, vol XI, no. 27, Sep 1996, pp. 97-107. Further research along the lines of #9, above.

17. "Belief revision and language splitting" in Proc. Logic, Language and Computation, Ed. Moss, Ginzburg and de Rijke, CSLI 1999, pp. 266-278 (earlier version appeared in 1996 in the preliminary proceedings).

The celebrated AGM axioms for belief revision allow the trivial revision under which all old information is lost. We show how we can incorporate a formal notion of relevance which allows one's information to be split uniquely into a number of disjoint subject areas. Revising information only in those areas where new information is received blocks the trivial revision.

18. "Length and structure of proofs," in Synthese 114, (1998), special issue edited by J. Hintikka.

A survey of work in the theory of proofs, beginning with our own work in the late sixties and early seventies and giving an account of subsequent results to date.

19. "Frege's puzzle and belief revision," typescript, November 1997. Presented at the World Congress of Philosophy, Boston 1998.

Ever since Frege there have been, largely unsuccessful, attempts to work out a notion of sense or meaning which will allow us to explain the cognitive contribution made by a sentence and also explain how its truth value is determined. Various puzzles, Frege's Hesperus-Phosphorus puzzle, Kripke's Pierre puzzle, Burge's arthritis puzzle, etc show up the difficulty of the problem. We show how an approach based on the notion of belief revision can address these various issues.

20. "Propositions, propositional attitudes and belief revision" to appear in Advances in Modal Logic, Volume 2, K. Segerberg, M. Zakharyaschev, M. de Rijke, H. Wansing, editors, CSLI Publications, 2000.
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This is a revised and expanded version of #19 above

21. "The Santa Fe bar problem revisited" (with Amy Greenwald and Bud Mishra), presented at the Stony Brook workshop on Game Theory, summer 1998.

The Santa Fe bar problem is a problem about a bar in Santa Fe New Mexico. The capacity of the bar is less than the number of people who want to go there but even people who do want to go, would not like to if it is crowded. This creates a game theoretic problem where it is impossible for the prospective customers to have a uniform strategy which can succeed. If everyone thinks that the bar will be crowded, then they will not go and the bar will be empty. If everyone thinks that the bar will be uncrowded, then they will go and the bar will in fact be crowded. Thus a uniform learning algorithm is not possible. We point out a similarity to the Russell paradox and investigate what kind of learning is possible.

22. "Sock Sorting," (with Laxmi Parida and Vaughan Pratt), appeared in a volume dedicated to Johan van Benthem electronically published by the University of Amsterdam.

If a person puts n pairs of socks in the washing machine and then the dryer, then when the wash is completed, what he has is 2*n individual socks. Socks which are near enough in color will seem to match, but this matching relation is not transitive. This results in the situation that naive matching can leave socks un-matched. So how can one match socks? One way is to try all possible matchings, and the problem looks on the face of it as if it can be NP-complete. But we show that there is a quadratic algorithm.

23. "An Inconsistency Tolerant Model for Belief Representation and Belief Revision," (with Samir Chopra), appeared in Proc. IJCAI 99.

We define the notion of a B-structure which consists of a number of theories with overlapping languages glued together. Such a structure allows us to localize an agent's beliefs as well as represent a situation where an agent's beliefs are globally incosistent but locally consistent. This model provides for both query answering and belief revision. Axioms analogous to those of AGM are satisfied.

24. "Non-Monotonic Inference on Sequenced Belief Bases", (with Samir Chopra and Konstantinos Georgatos), Proceedings of the Delphi Conference in Logic, July 1999.

We consider the approach to belief representation and belief revision where revision is taken to be the trivial operation of concatenation of new information. The logical sophistication will then be in the operation for answering queries. This is done using a maxi-consistent subset of previously received information, which gives priority to more recently received information as well as to more relevant information.

25."Two place probabilities, beliefs and belief revision: on the foundations of iterative belief kinematics", (with Horacio Arlo Costa), in Amsterdam Colloquium '99.

We extend some results of van Fraassen on two dimensional probabilities, sometimes called Popper functions. The idea is that $P(X,Y)$ gives the probability of $X$ relative to $Y$ and this notion can make sense even if the probability of $Y$ itself is 0. Van Fraassen defined a family of cores which represent various {\em Maginot lines for beliefs. I.e. they represent positions to which we fall back when some very surprising information is received. We give a complete characterization of the notion of cores for the case where the whole space is countable.