Annals of Mathematics and Artificial Intelligence - AMAI, 1999
The system presented here shows the feasibility of modeling the knowledge involved in a complex m... more The system presented here shows the feasibility of modeling the knowledge involved in a complex musical activity by integrating sub-symbolic and symbolic processes. This research focuses on the question of whether there is any advantage in integrating a neural network together with a distributed artificial intelligence approach within the music domain. The primary purpose of our work is to design a model that describes the different aspects a user might be interested in considering when involved in a musical activity. The approach we suggest in this work enables the musician to encode his knowledge, intuitions, and aesthetic taste into different modules. The system captures these aspects by computing and applying three distinct functions: rules, fuzzy concepts, and learning. As a case study, we began experimenting with first species two-part counterpoint melodies. We have developed a hybrid system composed of a connectionist module and an agent-based module to combine the sub-symbol...
This paper presents a substructural logic of sequents with very restricted exchange and weakening... more This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic structures include a binary relation that expresses orthogonality between elements and enables the definition of an operation that generalizes the projection operation in Hilbert spaces. The language has a unitary connective, a sort of negation, and two dual binary connectives that are neither commutative nor associative, sorts of conjunction and disjunction. This provides a logic for quantum measurements whose proof theory is aesthetically pleasing.
This paper proposes an original exchange property of valuations.This property is shown to be equi... more This paper proposes an original exchange property of valuations.This property is shown to be equivalent to a property described by Dress and Terhalle in the context of discrete optimization and matroids and shown there to characterize the valuations for which the demand oracle can be implemented by a greedy algorithm. The same exchange property is also equivalent to a property described independently by Reijnierse, van Gellekom and Potters and by Lehmann, Lehmann and Nisan and shown there to be satisfied by substitutes valuations. It studies the family of valuations that satisfy this exchange property, the ultra valuations. Any substitutes valuation is an ultra valuation, but ultra valuations may exhibit complementarities. Any symmetric valuation is an ultra valuation. Substitutes valuations are exactly the submodular ultra valuations. Ultra valuations define ultrametrics on the set of items. The maximum of an ultra valuation on $n$ items can be found in $O(n^2)$ steps. Finding an e...
Nielsen characterized in full those 2-party quantum protocols of local operations and classical c... more Nielsen characterized in full those 2-party quantum protocols of local operations and classical communication that transform, with probability one, a pure global initial state into a pure global final state. The present work considers the generalization of Nielsen's characterization to n-party protocols. It presents a sweeping generalization of the only if part of Nielsen's result. The result presented here pertains also to protocols that do not generate a final state for sure, it considers arbitrary mixed initial states instead of pure states and n-party protocols for an arbitrary n. In this very general setting, local operations and classical communication can never decrease the expected spectra of the local mixed states in the majorization ordering. In other terms, the local states can only become purer (weakly) in expectation. The proof also provides an improvement on Nielsen's. The if part of Nielsen's characterization does not generalize. This is shown by study...
I. INTRODUCTION 1. Background and Motivation One of the more important and active areas in the th... more I. INTRODUCTION 1. Background and Motivation One of the more important and active areas in the theory of programming languages is that of concurrent programs, specifically their design, definition, analysis, and verification. Due to recent developments in the technology of microprocessors, there is a trend toward languages supporting distributed activities involving communication rather than concurrent activities on some shared resources, mainly memory. Thus, it becomes very important to supply adequate tools for the definition and analysis of such programs and programming languages. One recent attempt to design such a language was done by Hoare [9], where the language CSP (communicating sequential processes) was presented informally. This is a language for the expression of nondeterministic, concurrent, and communicating programs.
characterization of some constructions relating to ordered and complete algebras is given. In par... more characterization of some constructions relating to ordered and complete algebras is given. In particular the completion of a poset and the initial objects of semivarieties of (complete) ordered algebras are studied. The quotient construction allows a reconciliation of the equational and synthetic (order-theoretic) approaches to abstract data types.
This paper proposes an original exchange property of valuations.This property is shown to be equi... more This paper proposes an original exchange property of valuations.This property is shown to be equivalent to a property described by Dress and Terhalle in the context of discrete optimization and matroids and shown there to characterize the valuations for which the demand oracle can be implemented by a greedy algorithm. The same exchange property is also equivalent to a property described independently by Reijnierse, van Gellekom and Potters and by Lehmann, Lehmann and Nisan and shown there to be satisfied by substitutes valuations. It studies the family of valuations that satisfy this exchange property, the ultra valuations. Any substitutes valuation is an ultra valuation, but ultra valuations may exhibit complementarities. Any symmetric valuation is an ultra valuation. Substitutes valuations are exactly the submodular ultra valuations. Ultra valuations define ultrametrics on the set of items. The maximum of an ultra valuation on n items can be found in O(n^2) steps. Finding an effic...
From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets'' was held i... more From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
It recently appeared to the author that the semantics of recursively defined data-types (from now... more It recently appeared to the author that the semantics of recursively defined data-types (from now on the term circularly defined data-types will be used to keep away from the "recursive function theory" connotation of the adjective "recursive") could benefit largely from the bulk of recent work on domain equations initiated by Dana Scott.
Suppose a knowledge base contains information on how the world generally behaves and in particula... more Suppose a knowledge base contains information on how the world generally behaves and in particular contains the information that birds, normally fly. Suppose that we obtain the information that Tweety is a bird, why should we conclude that it is plausible that Tweety flies? The answer to this question is unexpectedly sophisticated since the obvious substitution rule has to be rejected. Our answer to this question is based on an extension to predicate calculus of the ideas presented in [7]. Preferential consequence relations over predicate calculi are defined. In addition to the rules satisfied by those relations in the propositional case, they satisfy two rules dealing with quantifiers. These rules are not enough to enable us to conclude that Tweety flies. The rational closure construction defined in [7] should be generalized to the predicate calculus case and, in the rational closure, Tweety should fly.
Certain services may be provided in a continuous, one-dimensional, ordered range of dierent quali... more Certain services may be provided in a continuous, one-dimensional, ordered range of dierent qualities and a customer requiring a service of quality q can only be oered a quality superior or equal to q. Only a discrete set of dierent qualities will be oered, and a service provider will provide the same service (of xed quality b) to all customers requesting qualities of service inferior or equal to b. Assuming all services (of quality b) are priced identically, a monopolist will choose the qualities of service and the prices that maximize pro t but, under perfect competition, a service provider will choose the (inferior) quality of service that can be priced at the lowest price. Assuming signi cant economies of scale, two fundamentally dierent regimes are possible: either a number of dierent classes of service are oered (DC regime), or a unique class of service oers an unbounded quality of service (UC regime). The DC regime appears in one of two sub-regimes: one, BDC, in which a nite ...
It is shown that, in a pure exchange economy of indivisible objects, if the valuation of no trade... more It is shown that, in a pure exchange economy of indivisible objects, if the valuation of no trader exhibits complementarity and if there are many traders, none of them is inuential enough to inuence the market by himself, there exists a competitive (i.e., Walrasian) equilibrium.
When a physicist performs a quantic measurement, new information about the system at hand is gath... more When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the "and then" operation that combines old and new information. The "and then" connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the "and then" connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch (1969) satisfies all the properties studied in this paper. All properties satisfied ...
Truth Revelation in Approximately Ecient Combinatorial Auctions
Some important classical mechanisms considered in Microeconomics and Game Theory require the solu... more Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a dicult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms - in particular, their truth revelation properties - assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by ide...
24th Annual Symposium on Foundations of Computer Science (sfcs 1983), 1983
Decision procedures are provided for checking the satistlabllity of a formula in each of the thre... more Decision procedures are provided for checking the satistlabllity of a formula in each of the three systems TCg. reb and Tet defined In [LS].. The procedures tor TCg and Tel run in non-deterministic time 2 2 "" where n is the size of the formula and c is a constant. The procedure for Teb runs in non-deterministic time 2 20ft • A deterministic exponential lower bound is proved for the three systems. All three syst.ems are also shown to be PSPACE-hard using results of [SC]. Those decision procedures are not •as efficient as the deterministic (one or tW'o)-exponential time procedures proposed in [BMP]and [EH1] for different logics of branching time that are weaker than ours in expressive power. No elementary decision procedure is known for a logic of branching time that is as expressive as ours. The decision procedures of the probabilistic logics of [HS] run in deterministic exponential time but their language is essentially less expressive than ours.
Annals of Mathematics and Artificial Intelligence - AMAI, 1999
The system presented here shows the feasibility of modeling the knowledge involved in a complex m... more The system presented here shows the feasibility of modeling the knowledge involved in a complex musical activity by integrating sub-symbolic and symbolic processes. This research focuses on the question of whether there is any advantage in integrating a neural network together with a distributed artificial intelligence approach within the music domain. The primary purpose of our work is to design a model that describes the different aspects a user might be interested in considering when involved in a musical activity. The approach we suggest in this work enables the musician to encode his knowledge, intuitions, and aesthetic taste into different modules. The system captures these aspects by computing and applying three distinct functions: rules, fuzzy concepts, and learning. As a case study, we began experimenting with first species two-part counterpoint melodies. We have developed a hybrid system composed of a connectionist module and an agent-based module to combine the sub-symbol...
This paper presents a substructural logic of sequents with very restricted exchange and weakening... more This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic structures include a binary relation that expresses orthogonality between elements and enables the definition of an operation that generalizes the projection operation in Hilbert spaces. The language has a unitary connective, a sort of negation, and two dual binary connectives that are neither commutative nor associative, sorts of conjunction and disjunction. This provides a logic for quantum measurements whose proof theory is aesthetically pleasing.
This paper proposes an original exchange property of valuations.This property is shown to be equi... more This paper proposes an original exchange property of valuations.This property is shown to be equivalent to a property described by Dress and Terhalle in the context of discrete optimization and matroids and shown there to characterize the valuations for which the demand oracle can be implemented by a greedy algorithm. The same exchange property is also equivalent to a property described independently by Reijnierse, van Gellekom and Potters and by Lehmann, Lehmann and Nisan and shown there to be satisfied by substitutes valuations. It studies the family of valuations that satisfy this exchange property, the ultra valuations. Any substitutes valuation is an ultra valuation, but ultra valuations may exhibit complementarities. Any symmetric valuation is an ultra valuation. Substitutes valuations are exactly the submodular ultra valuations. Ultra valuations define ultrametrics on the set of items. The maximum of an ultra valuation on $n$ items can be found in $O(n^2)$ steps. Finding an e...
Nielsen characterized in full those 2-party quantum protocols of local operations and classical c... more Nielsen characterized in full those 2-party quantum protocols of local operations and classical communication that transform, with probability one, a pure global initial state into a pure global final state. The present work considers the generalization of Nielsen's characterization to n-party protocols. It presents a sweeping generalization of the only if part of Nielsen's result. The result presented here pertains also to protocols that do not generate a final state for sure, it considers arbitrary mixed initial states instead of pure states and n-party protocols for an arbitrary n. In this very general setting, local operations and classical communication can never decrease the expected spectra of the local mixed states in the majorization ordering. In other terms, the local states can only become purer (weakly) in expectation. The proof also provides an improvement on Nielsen's. The if part of Nielsen's characterization does not generalize. This is shown by study...
I. INTRODUCTION 1. Background and Motivation One of the more important and active areas in the th... more I. INTRODUCTION 1. Background and Motivation One of the more important and active areas in the theory of programming languages is that of concurrent programs, specifically their design, definition, analysis, and verification. Due to recent developments in the technology of microprocessors, there is a trend toward languages supporting distributed activities involving communication rather than concurrent activities on some shared resources, mainly memory. Thus, it becomes very important to supply adequate tools for the definition and analysis of such programs and programming languages. One recent attempt to design such a language was done by Hoare [9], where the language CSP (communicating sequential processes) was presented informally. This is a language for the expression of nondeterministic, concurrent, and communicating programs.
characterization of some constructions relating to ordered and complete algebras is given. In par... more characterization of some constructions relating to ordered and complete algebras is given. In particular the completion of a poset and the initial objects of semivarieties of (complete) ordered algebras are studied. The quotient construction allows a reconciliation of the equational and synthetic (order-theoretic) approaches to abstract data types.
This paper proposes an original exchange property of valuations.This property is shown to be equi... more This paper proposes an original exchange property of valuations.This property is shown to be equivalent to a property described by Dress and Terhalle in the context of discrete optimization and matroids and shown there to characterize the valuations for which the demand oracle can be implemented by a greedy algorithm. The same exchange property is also equivalent to a property described independently by Reijnierse, van Gellekom and Potters and by Lehmann, Lehmann and Nisan and shown there to be satisfied by substitutes valuations. It studies the family of valuations that satisfy this exchange property, the ultra valuations. Any substitutes valuation is an ultra valuation, but ultra valuations may exhibit complementarities. Any symmetric valuation is an ultra valuation. Substitutes valuations are exactly the submodular ultra valuations. Ultra valuations define ultrametrics on the set of items. The maximum of an ultra valuation on n items can be found in O(n^2) steps. Finding an effic...
From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets'' was held i... more From 03.01.05 to 07.01.05, the Dagstuhl Seminar 05011``Computing and Markets'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
It recently appeared to the author that the semantics of recursively defined data-types (from now... more It recently appeared to the author that the semantics of recursively defined data-types (from now on the term circularly defined data-types will be used to keep away from the "recursive function theory" connotation of the adjective "recursive") could benefit largely from the bulk of recent work on domain equations initiated by Dana Scott.
Suppose a knowledge base contains information on how the world generally behaves and in particula... more Suppose a knowledge base contains information on how the world generally behaves and in particular contains the information that birds, normally fly. Suppose that we obtain the information that Tweety is a bird, why should we conclude that it is plausible that Tweety flies? The answer to this question is unexpectedly sophisticated since the obvious substitution rule has to be rejected. Our answer to this question is based on an extension to predicate calculus of the ideas presented in [7]. Preferential consequence relations over predicate calculi are defined. In addition to the rules satisfied by those relations in the propositional case, they satisfy two rules dealing with quantifiers. These rules are not enough to enable us to conclude that Tweety flies. The rational closure construction defined in [7] should be generalized to the predicate calculus case and, in the rational closure, Tweety should fly.
Certain services may be provided in a continuous, one-dimensional, ordered range of dierent quali... more Certain services may be provided in a continuous, one-dimensional, ordered range of dierent qualities and a customer requiring a service of quality q can only be oered a quality superior or equal to q. Only a discrete set of dierent qualities will be oered, and a service provider will provide the same service (of xed quality b) to all customers requesting qualities of service inferior or equal to b. Assuming all services (of quality b) are priced identically, a monopolist will choose the qualities of service and the prices that maximize pro t but, under perfect competition, a service provider will choose the (inferior) quality of service that can be priced at the lowest price. Assuming signi cant economies of scale, two fundamentally dierent regimes are possible: either a number of dierent classes of service are oered (DC regime), or a unique class of service oers an unbounded quality of service (UC regime). The DC regime appears in one of two sub-regimes: one, BDC, in which a nite ...
It is shown that, in a pure exchange economy of indivisible objects, if the valuation of no trade... more It is shown that, in a pure exchange economy of indivisible objects, if the valuation of no trader exhibits complementarity and if there are many traders, none of them is inuential enough to inuence the market by himself, there exists a competitive (i.e., Walrasian) equilibrium.
When a physicist performs a quantic measurement, new information about the system at hand is gath... more When a physicist performs a quantic measurement, new information about the system at hand is gathered. This paper studies the logical properties of how this new information is combined with previous information. It presents Quantum Logic as a propositional logic under two connectives: negation and the "and then" operation that combines old and new information. The "and then" connective is neither commutative nor associative. Many properties of this logic are exhibited, and some small elegant subset is shown to imply all the properties considered. No independence or completeness result is claimed. Classical physical systems are exactly characterized by the commutativity, the associativity, or the monotonicity of the "and then" connective. Entailment is defined in this logic and can be proved to be a partial order. In orthomodular lattices, the operation proposed by Finch (1969) satisfies all the properties studied in this paper. All properties satisfied ...
Truth Revelation in Approximately Ecient Combinatorial Auctions
Some important classical mechanisms considered in Microeconomics and Game Theory require the solu... more Some important classical mechanisms considered in Microeconomics and Game Theory require the solution of a dicult optimization problem. This is true of mechanisms for combinatorial auctions, which have in recent years assumed practical importance, and in particular of the gold standard for combinatorial auctions, the Generalized Vickrey Auction (GVA). Traditional analysis of these mechanisms - in particular, their truth revelation properties - assumes that the optimization problems are solved precisely. In reality, these optimization problems can usually be solved only in an approximate fashion. We investigate the impact on such mechanisms of replacing exact solutions by approximate ones. Specically, we look at a particular greedy optimization method. We show that the GVA payment scheme does not provide for a truth revealing mechanism. We introduce another scheme that does guarantee truthfulness for a restricted class of players. We demonstrate the latter property by ide...
24th Annual Symposium on Foundations of Computer Science (sfcs 1983), 1983
Decision procedures are provided for checking the satistlabllity of a formula in each of the thre... more Decision procedures are provided for checking the satistlabllity of a formula in each of the three systems TCg. reb and Tet defined In [LS].. The procedures tor TCg and Tel run in non-deterministic time 2 2 "" where n is the size of the formula and c is a constant. The procedure for Teb runs in non-deterministic time 2 20ft • A deterministic exponential lower bound is proved for the three systems. All three syst.ems are also shown to be PSPACE-hard using results of [SC]. Those decision procedures are not •as efficient as the deterministic (one or tW'o)-exponential time procedures proposed in [BMP]and [EH1] for different logics of branching time that are weaker than ours in expressive power. No elementary decision procedure is known for a logic of branching time that is as expressive as ours. The decision procedures of the probabilistic logics of [HS] run in deterministic exponential time but their language is essentially less expressive than ours.
Uploads
Papers by Daniel Lehmann