We introduce a family of partial stable model semantics for logic programs with arbitrary aggrega... more We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in three-valued logic. Any semantics in this family satisfies two important properties: (i) it extends the partial stable semantics for normal logic programs and (ii) total stable models are always minimal. We also give a specific instance of the semantics and show that it has several attractive features.
We discuss work of Zdzisław Pawlak in the area of databases and the extension of that work to the... more We discuss work of Zdzisław Pawlak in the area of databases and the extension of that work to the theory of rough sets. In particular we look at his motivations for introducing information storage and retrieval systems and how this, eventually, led to rough sets theory.
We study properties of rough sets, that is, approximations to sets of records in a database or, m... more We study properties of rough sets, that is, approximations to sets of records in a database or, more formally, to subsets of the universe of an information system. A rough set is a pair hL; U i such that L; U are de nable in the information system and L U. In the paper, we introduce a language, called the language of inclusion-exclusion, to describe incomplete speci cations of (unknown) sets. We use rough sets in order to de ne a semantics for theories in the inclusion-exclusion language. We argue that our concept of a rough set is closely related to that introduced by Pawlak. We show that rough sets can be ordered by the knowledge ordering (denoted kn). We prove that Pawlak's rough sets are characterized as kn-greatest approximations. We show that for any consistent (that is, satis able) theory T in the language of inclusion-exclusion there exists a kn-greatest rough set approximating all sets X that satisfy T. For some classes of theories in the language of inclusion-exclusion, we provide algorithmic ways to nd this best approximation. We also state a number of miscellaneous results and discuss some open problems.
We investigate the operators associated with approximations in the rough set theory introduced by... more We investigate the operators associated with approximations in the rough set theory introduced by Pawlak in his (Paw82,MP84) and extensively stud- ied by the Rough Set community (RS06). We use universal algebra techniques to establish a natural characterization of operators associated with rough s ets.
Background: The American Board of Family Practice is developing a computer-based recertification ... more Background: The American Board of Family Practice is developing a computer-based recertification process. An optimal implementation requires a formal model of family medicine, which will become the basis for a knowledge base. Design: The proposed model of family medicine contains six entities: Population, Record, Agents of Change, Health States, Findings, and Courses of Action. The model illustrates 15 important relations between entities. For instance: Health States Lead to Health States, and Findings Associate with Health States. These two relations describe natural history, manifestations of disease, and the effects of medical interventions and risk factors. Because time is such an important aspect of primary care, nearly all numeric data are represented as graphs of possible values over time, called Patterns, which include details about periodicity. Patterns and other aspects of the model provide a means of describing covariance between observations, such as the influence of height on weight. Results: The model reflects many family practice activities and suggests some formal descriptions of family practice. For instance, diagnostic activities focus largely on classifying early or short segments of Patterns in Findings. Most medical interventions attempt to alter either the probability distributions in a Lead-to relation or the impact of a Finding. Conclusion: The proposed model of family medicine could find uses in many applications, including computer-based tests, medical records, reference systems, and decision support tools. 0 Am Board Fam Pract 1996; 9:41-52.) The American medical specialty boards certify physicians to practice medicine in their respective fields. In theory, board certification indicates at least minimal competence in an area of advanced training. Minimal competence is not precisely defined. The American Board of Family Practice (ABFP) currently administers paper-based certification and recertification examinations. These examinations contain conventional item formats, case descriptions, and still photographs. Recertification examinations allow physicians to select portions of the test according to their interests. Both examinations intend to engage and test problem-solving skills, disease recognition, and fact retention. The ABFP would like to expand its testing process to (1) allow testing at remote sites and
We introduce a family of partial stable model semantics for logic programs with arbitrary aggrega... more We introduce a family of partial stable model semantics for logic programs with arbitrary aggregate relations. The semantics are parametrized by the interpretation of aggregate relations in three-valued logic. Any semantics in this family satisfies two important properties: (i) it extends the partial stable semantics for normal logic programs and (ii) total stable models are always minimal. We also give a specific instance of the semantics and show that it has several attractive features.
We discuss work of Zdzisław Pawlak in the area of databases and the extension of that work to the... more We discuss work of Zdzisław Pawlak in the area of databases and the extension of that work to the theory of rough sets. In particular we look at his motivations for introducing information storage and retrieval systems and how this, eventually, led to rough sets theory.
We study properties of rough sets, that is, approximations to sets of records in a database or, m... more We study properties of rough sets, that is, approximations to sets of records in a database or, more formally, to subsets of the universe of an information system. A rough set is a pair hL; U i such that L; U are de nable in the information system and L U. In the paper, we introduce a language, called the language of inclusion-exclusion, to describe incomplete speci cations of (unknown) sets. We use rough sets in order to de ne a semantics for theories in the inclusion-exclusion language. We argue that our concept of a rough set is closely related to that introduced by Pawlak. We show that rough sets can be ordered by the knowledge ordering (denoted kn). We prove that Pawlak's rough sets are characterized as kn-greatest approximations. We show that for any consistent (that is, satis able) theory T in the language of inclusion-exclusion there exists a kn-greatest rough set approximating all sets X that satisfy T. For some classes of theories in the language of inclusion-exclusion, we provide algorithmic ways to nd this best approximation. We also state a number of miscellaneous results and discuss some open problems.
We investigate the operators associated with approximations in the rough set theory introduced by... more We investigate the operators associated with approximations in the rough set theory introduced by Pawlak in his (Paw82,MP84) and extensively stud- ied by the Rough Set community (RS06). We use universal algebra techniques to establish a natural characterization of operators associated with rough s ets.
Background: The American Board of Family Practice is developing a computer-based recertification ... more Background: The American Board of Family Practice is developing a computer-based recertification process. An optimal implementation requires a formal model of family medicine, which will become the basis for a knowledge base. Design: The proposed model of family medicine contains six entities: Population, Record, Agents of Change, Health States, Findings, and Courses of Action. The model illustrates 15 important relations between entities. For instance: Health States Lead to Health States, and Findings Associate with Health States. These two relations describe natural history, manifestations of disease, and the effects of medical interventions and risk factors. Because time is such an important aspect of primary care, nearly all numeric data are represented as graphs of possible values over time, called Patterns, which include details about periodicity. Patterns and other aspects of the model provide a means of describing covariance between observations, such as the influence of height on weight. Results: The model reflects many family practice activities and suggests some formal descriptions of family practice. For instance, diagnostic activities focus largely on classifying early or short segments of Patterns in Findings. Most medical interventions attempt to alter either the probability distributions in a Lead-to relation or the impact of a Finding. Conclusion: The proposed model of family medicine could find uses in many applications, including computer-based tests, medical records, reference systems, and decision support tools. 0 Am Board Fam Pract 1996; 9:41-52.) The American medical specialty boards certify physicians to practice medicine in their respective fields. In theory, board certification indicates at least minimal competence in an area of advanced training. Minimal competence is not precisely defined. The American Board of Family Practice (ABFP) currently administers paper-based certification and recertification examinations. These examinations contain conventional item formats, case descriptions, and still photographs. Recertification examinations allow physicians to select portions of the test according to their interests. Both examinations intend to engage and test problem-solving skills, disease recognition, and fact retention. The ABFP would like to expand its testing process to (1) allow testing at remote sites and
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