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422
The Semantics Of Constraint Logic Programs
 JOURNAL OF LOGIC PROGRAMMING
, 1996
"... This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and comp ..."
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Cited by 872 (14 self)
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This paper presents for the first time the semantic foundations of CLP in a selfcontained and complete package. The main contributions are threefold. First, we extend the original conference paper by presenting definitions and basic semantic constructs from first principles, giving new and complete proofs for the main lemmas. Importantly, we clarify which theorems depend on conditions such as solution compactness, satisfaction completeness and independence of constraints. Second, we generalize the original results to allow for incompleteness of the constraint solver. This is important since almost all CLP systems use an incomplete solver. Third, we give conditions on the (possibly incomplete) solver which ensure that the operational semantics is confluent, that is, has independence of literal scheduling.
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 413 (50 self)
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This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include constrained linear systems, finite state machines, some classes of discrete event systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting online optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP), for which e#cient solvers have been recently developed. Some examples and a simulation case s...
A logic for reasoning about probabilities.
 Information and Computation
, 1990
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Valid conjunction inference with the minimum statistic. NeuroImage 25, 653–660
, 2005
"... In logic a conjunction is defined as an AND between truth statements. In neuroimaging, investigators may look for brain areas activated by task A AND by task B, or a conjunction of tasks (Price & Friston, 1997). Friston et al. (1999b) introduced a minimum statistic test for conjunction. We refer ..."
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Cited by 256 (4 self)
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In logic a conjunction is defined as an AND between truth statements. In neuroimaging, investigators may look for brain areas activated by task A AND by task B, or a conjunction of tasks (Price & Friston, 1997). Friston et al. (1999b) introduced a minimum statistic test for conjunction. We refer to this method as the minimum statistic compared to the global null (MS/GN). The MS/GN is implemented in SPM2 and SPM99 software, and has been widely used as a test of conjunction. However, we assert that it does not have the correct null hypothesis for a test of logical AND, and further, this has led to confusion in the neuroimaging community. In this paper, we define a conjunction and explain the problem with the MS/GN test as a conjunction method. We present a survey of recent practice in neuroimaging which reveals that the MS/GN test is very often misinterpreted as evidence of a logical AND. We show that a correct test for a logical AND requires that all the comparisons in the conjunction are individually significant. This result holds even if the comparisons are not independent. We suggest that the revised test proposed here is the appropriate means for conjunction inference in neuroimaging. Nichols, et al. Valid Conjunction Inference with the Minimum Statistic 3 1
Logic and databases: a deductive approach
 ACM Computing Surveys
, 1984
"... The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling ..."
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Cited by 170 (2 self)
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The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems. There are two main parts to the paper, devoted respectively to conventional databases and deductive databases. In the first part, we focus on query languages, integrity modeling and maintenance, query optimization, and data
Explicit Provability And Constructive Semantics
 Bulletin of Symbolic Logic
, 2001
"... In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus is noth ..."
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Cited by 139 (25 self)
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In 1933 G odel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that G odel's provability calculus is nothing but the forgetful projection of LP. This also achieves G odel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a BrouwerHeytingKolmogorov style provability semantics for Int which resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and #calculus.
Internal set theory: A new approach to nonstandard analysis
 Bull. Amer. Math. Soc
, 1977
"... 1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making these powerful methods readily available to the working mathematician. This approach to nonstandard analysis is based on a theory which we call internal set theory (1ST) ..."
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Cited by 110 (0 self)
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1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making these powerful methods readily available to the working mathematician. This approach to nonstandard analysis is based on a theory which we call internal set theory (1ST). We start with axiomatic set theory, say ZFC (ZermeloFraenkel set theory with the axiom of choice [1]). In addition to the usual undefined binary predicate E of set theory we adjoin a new undefined unary predicate standard. The axioms of 1ST are the usual axioms of ZFC plus three others, which we will state below. All theorems of conventional mathematics remain valid. No change in terminology is required. What is new in internal set theory is only an addition, not a change. We choose to call certain sets standard (and we recall that in ZFC every mathematical objecta real number, a function, etc.is a set), but the theorems of conventional mathematics apply to all sets, nonstandard as well as standard.
Simple Consequence Relations
 Information and Computation
, 1991
"... We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (incl ..."
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Cited by 107 (19 self)
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We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and nonmonotonic logics) and for a general, semanticsindependent classification of standard connectives via equations on consequence relations (these include Girard's "multiplicatives" and "additives"). We next investigate the standard methods for uniformly representing consequence relations: Hilbert type, Natural Deduction and Gentzen type. The advantages and disadvantages of using each system and what should be taken as good representations in each case (especially from the implementation point of view) are explained. We end by briefly outlining (with examples) some methods for developing nonuniform, but still efficient, representations of consequence relations.
C.: The SMTLIB Standard: Version 2.0
, 2010
"... Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified ver ..."
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Cited by 102 (11 self)
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Permission is granted to anyone to make or distribute verbatim copies of this document, in any medium, provided that the copyright notice and permission notice are preserved, and that the distributor grants the recipient permission for further redistribution as permitted by this notice. Modified versions may not be made. Preface The SMTLIB initiative is an international effort, supported by several research groups worldwide, with the twofold goal of producing an extensive online library of benchmarks and promoting the adoption of common languages and interfaces for SMT solvers. This document specifies Version 2.0 of the SMTLIB Standard. This is a major upgrade of the previous version, Version 1.2, which, in addition to simplifying and extending the languages of that version, includes a new command language for interfacing with SMT solvers. Acknowledgments Version 2.0 of the SMTLIB standard was developed with the input of the whole SMT community and three international work groups consisting of developers and users of SMT tools: the SMTAPI work group, led by A. Stump, the SMTLOGIC work group, led by C. Tinelli, the SMTMODELS work group, led by C. Barrett. Particular thanks are due to the following work group members, who contributed numerous
Reasoning Situated in Time I: Basic Concepts
, 1990
"... The needs of a realtime reasoner situated in an environment may make it appropriate to view errorcorrection and nonmonotonicity as much the same thing. This has led us to formulate situated (or step) logic, an approach to reasoning in which the formalism has a kind of realtime selfreference tha ..."
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Cited by 101 (44 self)
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The needs of a realtime reasoner situated in an environment may make it appropriate to view errorcorrection and nonmonotonicity as much the same thing. This has led us to formulate situated (or step) logic, an approach to reasoning in which the formalism has a kind of realtime selfreference that affects the course of deduction itself. Here we seek to motivate this as a useful vehicle for exploring certain issues in commonsensereasoning. In particular, a chief drawback of more traditional logics is avoided: from a contradiction we do not have all wffs swamping the (growing) conclusion set. Rather, we seek potentially inconsistent, but nevertheless useful, logics where the realtime selfreferential feature allows a direct contradiction to be spotted and corrective action taken, as part of the same system of reasoning. Some specific inference mechanisms for realtime default reasoning are suggested, notably a form of introspection relevant to default reasoning. Special treatment of ...