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15
A TemporalInteractivist Perspective on the Dynamics of Mental States
 COGNITIVE SYSTEMS RESEARCH JOURNAL
, 2003
"... This paper addresses the dynamics of mental states in relation to the dynamics of the interaction with the external world. It contributes a formalised temporalinteractivist approach to these dynamics based on temporal traces for semantics and a temporal trace language to provide an expressive means ..."
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Cited by 36 (27 self)
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This paper addresses the dynamics of mental states in relation to the dynamics of the interaction with the external world. It contributes a formalised temporalinteractivist approach to these dynamics based on temporal traces for semantics and a temporal trace language to provide an expressive means to formulate dynamic properties. The approach provides both a foundation for the dynamical and interactivist perspective on cognitive phenomena, and a supporting software environment for practical application.
Mechanical Verification of a Square Root Algorithm Using Taylor’s Theorem
 In Formal Methods in Computer Aided Design (FMCAD'02
, 2002
"... Abstract. The IBM Power4 TM processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theore ..."
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Cited by 5 (1 self)
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Abstract. The IBM Power4 TM processor uses series approximation to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis of the approximation error on a Chebyshev series. This is done by proving Taylor’s theorem, and then analyzing the Chebyshev series using Taylor series. Taylor’s theorem is proved by way of nonstandard analysis, as implemented in ACL2(r). Since Taylor series of a given order have less accuracy than Chebyshev series in general, we used hundreds of Taylor series generated by ACL2(r) to evaluate the error of a Chebyshev series. 1
Taylor's Formula with Remainder
 In Proceedings of the Third International Workshop of the ACL2 Theorem Prover and its Applications
, 2002
"... In this paper, we present a proof in ACL2(r) of Taylor's formula with remainder. ..."
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Cited by 4 (4 self)
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In this paper, we present a proof in ACL2(r) of Taylor's formula with remainder.
An ACL2 Tutorial
"... Abstract. We describe a tutorial that demonstrates the use of the ACL2 theorem prover. We have three goals: to enable a motivated reader to start on a path towards effective use of ACL2; to provide ideas for other interactive theorem prover projects; and to elicit feedback on how we might incorporat ..."
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Cited by 4 (1 self)
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Abstract. We describe a tutorial that demonstrates the use of the ACL2 theorem prover. We have three goals: to enable a motivated reader to start on a path towards effective use of ACL2; to provide ideas for other interactive theorem prover projects; and to elicit feedback on how we might incorporate features of other proof tools into ACL2. 1
Formal Proof of a Wave Equation Resolution Scheme: the Method Error ⋆
"... Abstract. Popular finite difference numerical schemes for the resolution of the onedimensional acoustic wave equation are wellknown to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper d ..."
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Cited by 4 (2 self)
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Abstract. Popular finite difference numerical schemes for the resolution of the onedimensional acoustic wave equation are wellknown to be convergent. We present a comprehensive formalization of the simplest scheme and formally prove its convergence in Coq. The main difficulties lie in the proper definition of asymptotic behaviors and the implicit way they are handled in the mathematical penandpaper proofs. To our knowledge, this is the first time this kind of mathematical proof is machinechecked. Key words: partial differential equation, acoustic wave equation, numerical scheme, Coq formal proofs 1
Formally Verifying an Algorithm Based on Interval Arithmetic for Checking Transversality
 IN: FIFTH INTERNATIONAL WORKSHOP ON THE ACL2 THEOREM PROVER AND ITS APPLICATIONS
, 2004
"... In this paper we use ACL2 to formally verify the correctness of an algorithm used in the analysis of dynamical systems. The algorithm uses interval arithmetic to check that a given vector field is transverse (nontangential) to an edge (line segment). Instead of operating on numbers, interval opera ..."
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Cited by 2 (0 self)
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In this paper we use ACL2 to formally verify the correctness of an algorithm used in the analysis of dynamical systems. The algorithm uses interval arithmetic to check that a given vector field is transverse (nontangential) to an edge (line segment). Instead of operating on numbers, interval operations operate on intervals, and they are guaranteed to return an overapproximation of the actual answer, thereby allowing us to use floating point arithmetic in a safe way. In this paper we prove that if the algorithm identifies an edge as transverse, then it is in fact transverse, as long as the underlying interval arithmetic operations are correctly implemented.
Theory Extension in ACL2(r)
"... Abstract. ACL2(r) is a modified version of the theorem prover ACL2 that adds support for the irrational numbers using nonstandard analysis. It has been used to prove basic theorems of analysis, as well as the correctness of the implementation of transcendental functions in hardware. This paper pres ..."
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Cited by 2 (1 self)
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Abstract. ACL2(r) is a modified version of the theorem prover ACL2 that adds support for the irrational numbers using nonstandard analysis. It has been used to prove basic theorems of analysis, as well as the correctness of the implementation of transcendental functions in hardware. This paper presents the logical foundations of ACL2(r). These foundations are also used to justify significant enhancements to ACL2(r). 1.
Coordination Approaches for Complex Software Systems
"... This document presents the results of a collaboration between the Vrije Universiteit Amsterdam, Department of Artificial Intelligence and Force Vision to investigate coordination approaches for complex software systems. The project was funded by Force Vision. More in particular, the following people ..."
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Cited by 1 (1 self)
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This document presents the results of a collaboration between the Vrije Universiteit Amsterdam, Department of Artificial Intelligence and Force Vision to investigate coordination approaches for complex software systems. The project was funded by Force Vision. More in particular, the following people participated: Force Vision: Rob Duell, Andy van der Mee, and Bas Vermeulen.
AgentOriented Modeling of the Dynamics of Complex Biological Processes I: Single Agent Models
 In press
, 2002
"... In the pair of papers of which this is Part I, the agentoriented modeling perspective to cope with biological complexity is discussed. Three levels of dynamics are distinguished and related to each other: dynamics of externally observable agent behavior, dynamics of internal agent processes, and ..."
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In the pair of papers of which this is Part I, the agentoriented modeling perspective to cope with biological complexity is discussed. Three levels of dynamics are distinguished and related to each other: dynamics of externally observable agent behavior, dynamics of internal agent processes, and dynamics of multiagent organisations. Basic agent concepts to describe externally observable agent behavior are introduced. In the context of the two case studies on animal behavior and cell functioning, it is shown how these concepts can be used to specify dynamic properties. In addition, a number of basic agent concepts to describe an agent's internal processes are introduced. Also these concepts are illustrated for specification of dynamic properties in the two case studies. Furthermore, the relationships between dynamic properties of externally observable behavior and dynamic properties of internal agent processes are addressed and illustrated for the animal and cell case studies. In the second paper, Part II, the dynamics within an organisation of multiple agents are addressed. Associated to the organisational structure, dynamic properties at different levels of aggregation are presented, related to each other, and illustrated for a third case study: the organisation of the circulatory system in mammals.
Improving Real Analysis in Coq: a UserFriendly Approach to Integrals and Derivatives ⋆
"... Abstract. Verification of numerical analysis programs requires dealing with derivatives and integrals. High confidence in this process can be achieved using a formal proof checker, such as Coq. Its standard library provides an axiomatization of real numbers and various lemmas about real analysis, wh ..."
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Abstract. Verification of numerical analysis programs requires dealing with derivatives and integrals. High confidence in this process can be achieved using a formal proof checker, such as Coq. Its standard library provides an axiomatization of real numbers and various lemmas about real analysis, which may be used for this purpose. Unfortunately, its definitions of derivative and integral are unpractical as they are partial functions that demand a proof term. This proof term makes the handling of mathematical formulas cumbersome and does not conform to traditional analysis. Other proof assistants usually do not suffer from this issue; for instance, they may rely on Hilbert’s epsilon to get total operators. In this paper, we propose a way to define total operators for derivative and integral without having to extend Coq’s standard axiomatization of real numbers. We proved the compatibility of our definitions with the standard library’s in order to leverage existing results. We also greatly improved automation for real analysis proofs that use Coq standard definitions. We exercised our approach on lemmas involving iterated partial derivatives and differentiation under the integral sign, that were missing from the formal proof of a numerical program solving the wave equation. 1