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A Many-valued Logic for Lexicographic Preference Representation

Angelos Charalambidis, George Papadimitriou, Panos Rondogiannis, Antonis Troumpoukis
2021 Proceedings of the Eighteenth International Conference on Principles of Knowledge Representation and Reasoning   unpublished
We introduce lexicographic logic, an extension of propositional logic that can represent a variety of preferences, most notably lexicographic ones.  ...  We demonstrate that, despite the well-known theoretical limitations that pose barriers to the quantitative representation of lexicographic preferences, there exists a subset of the rational numbers over  ...  implementing qualitative preferences in deductive querying systems" (5048151).  ... 
doi:10.24963/kr.2021/62 fatcat:sd2oo4qo7vc2pg2x2n325dh4f4

Lexicographic priorities in default logic

Jussi Rintanen
1998 Artificial Intelligence  
Given a default theory and a partial ordering on the defaults, the preferred extensions are the lexicographically best extensions.  ...  This work extends Reiter's default logic with a priority mechanism that is based on lexicographic comparison.  ...  Hence 7 is a A, P-ordering for E, and E is a P-preferred extension of A. 0 Reiter's default logic is a special case of prioritized default logic.  ... 
doi:10.1016/s0004-3702(98)00097-6 fatcat:pjjnmgroorcbhcjygupr4paqke

Reliability-based preference dynamics: lexicographic upgrade

Fernando R Velázquez-Quesada
2017 Journal of Logic and Computation  
More precisely, it considers agents with a preference ordering over a set of objects and a reliability ordering over the agents themselves, providing a logical framework describing the way in which the  ...  The main results are the definitions of this lexicographic upgrade for diverse types of reliability relations (in particular, the preorder and total preorder cases), a sound and complete axiom system for  ...  The proposal of this paper differs from threshold models in that what matters for an agent is not how many people has a given preference, but rather the preferences of certain people (namely, those she  ... 
doi:10.1093/logcom/exx019 fatcat:zyvbsca7vfemvarnjbuoydhuxu

Lexicographically-ordered constraint satisfaction problems

Eugene C. Freuder, Robert Heffernan, Richard J. Wallace, Nic Wilson
2009 Constraints  
Preferences are represented as a lexicographic order over complete assignments based on variable importance and rankings of values in each domain.  ...  We describe a simple CSP formalism for handling multi-attribute preference problems with hard constraints, one that combines hard constraints and preferences so the two are easily distinguished conceptually  ...  By using a qualitative representation in this context, we circumvent many difficult issues regarding the validity of a preference representation that arise when one associates numerical values with CSP  ... 
doi:10.1007/s10601-009-9069-0 fatcat:3hju3xvxyjfwtksjuk4tggldw4

Nonstandard utilities for lexicographically decomposable orderings

Davide Rizza
2015 Journal of Mathematical Economics  
Using a basic theorem from mathematical logic, I show that there are field-extensions of R on which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably  ...  Then there are uncountably many * Rvalued utility functions for X • L Z.  ...  If every cell in its lexicographic decomposition has a R-valued utility function, then Z has uncountably many * R-valued utility functions.Moreover, if Z is non-representable, then the utility functions  ... 
doi:10.1016/j.jmateco.2015.06.012 fatcat:kqoqpmyekbdxvaywbg5aftf76q

Learning Optimal and Near-Optimal Lexicographic Preference Lists [article]

Ahmed Moussa, Xudong Liu
2019 arXiv   pre-print
We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists).  ...  Given a set of examples that are pairwise ordinal preferences over a universe of objects built of attributes of discrete values, we want to learn (1) an optimal LP-list that decides the maximum number  ...  We focus on a particular lexicographic preference model, called lexicographic preference lists, or LP-lists for short, an intuitive and concise model describing the importance ordering of the attributes  ... 
arXiv:1909.09072v1 fatcat:r4prscdpxnc4lgytfcjfahzzam

Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs [chapter]

Umberto Straccia
2008 Lecture Notes in Computer Science  
Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages.  ...  We refer the reader to [92, 93, 95] for algorithms for many-valued logics. Table 1 .  ...  Many-Valued Logics In the setting of many-valued logics, the convention prescribing that a proposition is either true or false is changed.  ... 
doi:10.1007/978-3-540-85658-0_2 fatcat:6ijgfocetbfixonkur2lrnabjy

Democratic approximation of lexicographic preference models

Fusun Yaman, Thomas J. Walsh, Michael L. Littman, Marie desJardins
2011 Artificial Intelligence  
Lexicographic preference models (LPMs) are an intuitive representation that corresponds to many real-world preferences exhibited by human decision makers.  ...  Previous algorithms for learning LPMs produce a "best guess" LPM that is consistent with the observations. Our approach is more democratic: we do not commit to a single LPM.  ...  Introduction Lexicographic preference models (LPMs) are one of the simplest yet most intuitive preference representations.  ... 
doi:10.1016/j.artint.2010.11.012 fatcat:ysfh4bx2pzdnbdqcojf7x4w6xm

Democratic approximation of lexicographic preference models

Fusun Yaman, Thomas J. Walsh, Michael L. Littman, Marie desJardins
2008 Proceedings of the 25th international conference on Machine learning - ICML '08  
Lexicographic preference models (LPMs) are an intuitive representation that corresponds to many real-world preferences exhibited by human decision makers.  ...  Previous algorithms for learning LPMs produce a "best guess" LPM that is consistent with the observations. Our approach is more democratic: we do not commit to a single LPM.  ...  Introduction Lexicographic preference models (LPMs) are one of the simplest yet most intuitive preference representations.  ... 
doi:10.1145/1390156.1390307 dblp:conf/icml/YamanWLd08 fatcat:fhgho6mm3bbgzjk3zlsk3bjrha

Choice by lexicographic semiorders

Paola Manzini, Marco Mariotti
2012 Theoretical Economics  
Choice by Lexicographic Semiorders * We propose an extension of Tversky's lexicographic semiorder to a model of boundedly rational choice.  ...  JEL Classification: D0 * Endless discussions on related matters with Michael Mandler were crucially helpful in shaping our ideas for this paper.  ...  via 1000 steps to recognise that x is better, as a representation by simple rationales would require.  ... 
doi:10.3982/te679 fatcat:76namtafsvfmdjybiox5kse7aq

Conditional lexicographic orders in constraint satisfaction problems

Richard J. Wallace, Nic Wilson
2008 Annals of Operations Research  
Rights Abstract The lexicographically-ordered CSP ("lexicographic CSP" or "LO-CSP" for short) combines a simple representation of preferences with the feasibility constraints of ordinary CSPs.  ...  In the first, for each conditional preference relation, the parents have higher priority than the children in the original lexicographic ordering.  ...  We are grateful to the editors and referees for their comments and suggestions, which helped improve the exposition of this paper.  ... 
doi:10.1007/s10479-008-0385-3 fatcat:d2vois6fnfd2helkndkb7yjnba

Lexicographic Enumeration of Set Partitions [article]

Giorgos Stamatelatos, Pavlos S. Efraimidis
2021 arXiv   pre-print
These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in modern high-level programming languages, without recursive structures and jump logic.  ...  This work is an aid for learners approaching this enumeration problem and programmers undertaking the task of implementing it.  ...  These partitions are also presented here in lexicographic order in respect to their restricted growth string representation.  ... 
arXiv:2105.07472v1 fatcat:jyglrueyxvhlrkcgzcim5mkbo4

FAst generation of lexicographic satisfiable assignments

Ana Petkovska, Alan Mishchenko, Mathias Soeken, Giovanni De Micheli, Robert Brayton, Paolo Ienne
2016 Proceedings of the 35th International Conference on Computer-Aided Design - ICCAD '16  
Given a variable order, LEXSAT finds a satisfying assignment whose integer value under the given variable order is minimum (maximum) among all satisfiable assignments.  ...  Lexicographic Boolean satisfiability (LEXSAT) is a variation of the Boolean satisfiability problem (SAT).  ...  A canonical representation is a unique representation for a function under certain conditions.  ... 
doi:10.1145/2966986.2967040 dblp:conf/iccad/PetkovskaMSMBI16 fatcat:av3senw2xbd5dger2uy3lprbv4

Qualitative choice logic

Gerhard Brewka, Salem Benferhat, Daniel Le Berre
2004 Artificial Intelligence  
Qualitative choice logic (QCL) is a propositional logic for representing alternative, ranked options for problem solutions.  ...  The semantics of qualitative choice logic is based on a preference relation among models.  ...  Acknowledgements We would like to thank Jérôme Lang, David Makinson, Pierre Marquis, Ilkka Niemelä, Leon van der Torre and the anonymous referees for very helpful comments.  ... 
doi:10.1016/j.artint.2004.04.006 fatcat:hbwiyot3hnh63olc5c6cneiavm

Nash Equilibria in Concurrent Games with Lexicographic Preferences

Julian Gutierrez, Aniello Murano, Giuseppe Perelli, Sasha Rubin, Michael Wooldridge
2017 Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence  
We study concurrent games with finite-memory strategies where players are given a Buchi and a mean-payoff objective, which are related by a lexicographic order: a player first prefers to satisfy its Buchi  ...  objective, and then prefers to minimise costs, which are given by a mean-payoff function.  ...  This limits the applicability of such representations for modelling many situations of interest.  ... 
doi:10.24963/ijcai.2017/148 dblp:conf/ijcai/0001MPRW17 fatcat:ulkmuv7zmzfflof737meid6yda
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