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31
A Relevant Analysis of Natural Deduction
 Journal of Logic and Computation
, 1999
"... Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and ..."
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Cited by 28 (7 self)
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Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lLcalculus; the representation mechanism is judgementsastypes, developed for relevant logics. The lLcalculus type theory is a firstorder dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required prooftheoretic metatheory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I calculus and ML with references. We describe the CurryHowardde Bruijn correspondence of the lLcalculus with a s...
A universal characterization of the closed euclidean interval (Extended Abstract)
 PROC. OF 16TH ANN. IEEE SYMP. ON LOGIC IN COMPUTER SCIENCE, LICS'01
, 2001
"... We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basi ..."
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Cited by 19 (1 self)
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We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. The universal property gives rise to an analogue of primitive recursion for defining computable functions on the interval. We use this to define basic arithmetic operations and to verify equations between them. We test the notion in categories of interest. In the
Recursive coalgebras from comonads
 Inform. and Comput
, 2006
"... The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of struct ..."
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Cited by 15 (3 self)
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The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and, centrally, give new conditions for the recursiveness of a coalgebra based on comonads, comonadcoalgebras and distributive laws of functors over comonads. We also present an alternative construction using countable products instead of cofree comonads.
Obstacle Avoidance as a Consequence of Suppressing Irreversible Actions
"... The observation that abstract principles can produce useful concrete behaviours is not new. In (Kaplan and Oudeyer, 2003) a number of basic visual motivational principles based on prediction errors. The general idea is to identify principles that can be expressed without reference to the ground mean ..."
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Cited by 1 (1 self)
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The observation that abstract principles can produce useful concrete behaviours is not new. In (Kaplan and Oudeyer, 2003) a number of basic visual motivational principles based on prediction errors. The general idea is to identify principles that can be expressed without reference to the ground meaning of sensormotor values, with the expectation that code based on such principles will function reliably in a broad range of environments and on different robots. We began, rather ambitiously, with the idea of capturing, in a single principle, absolutely everything a domestic robot should avoid doing: do not do what you cannot undo! We then discovered that, when this
Efficient node overlap removal using a proximity stress model
 In 16th Symp. on Graph Drawing (GD
, 2008
"... Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a postprocessing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using li ..."
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Cited by 13 (6 self)
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Abstract. When drawing graphs whose nodes contain text or graphics, the nontrivial node sizes must be taken into account, either as part of the initial layout or as a postprocessing step. The core problem is to avoid overlaps while retaining the structural information inherent in a layout using little additional area. This paper presents a new node overlap removal algorithm that does well by these measures. 1
Logical Relations and Data Abstraction
 Proc. Computer Science Logic, CSL 2000, Fischbachau. Springer LNCS 1862
, 1996
"... We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suita ..."
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Cited by 4 (1 self)
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We prove, in the context of simple type theory, that logical relations are sound and complete for data abstraction as given by equational specifications. Specifically, we show that two implementations of an equationally specified abstract type are equivalent if and only if they are linked by a suitable logical relation. This allows us to introduce new types and operations of any order on those types, and to impose equations between terms of any order. Implementations are required to respect these equations up to a general form of contextual equivalence, and two implementations are equivalent if they produce the same contextual equivalence on terms of the enlarged language. Logical relations are introduced abstractly, soundness is almost automatic, but completeness is more difficult, achieved using a variant of Jung and Tiuryn's logical relations of varying arity. The results are expressed and proved categorically.
Corecursive Algebras: A Study of General Structured Corecursion (Extended Abstract)
"... Abstract. We study general structured corecursion, dualizing the work of Osius, Taylor, and others on general structured recursion. We call an algebra of a functor corecursive if it supports general structured corecursion: there is a unique map to it from any coalgebra of the same functor. The conce ..."
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Cited by 3 (1 self)
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Abstract. We study general structured corecursion, dualizing the work of Osius, Taylor, and others on general structured recursion. We call an algebra of a functor corecursive if it supports general structured corecursion: there is a unique map to it from any coalgebra of the same functor. The concept of antifounded algebra is a statement of the bisimulation principle. We show that it is independent from corecursiveness: Neither condition implies the other. Finally, we call an algebra focusing if its codomain can be reconstructed by iterating structural refinement. This is the strongest condition and implies all the others. 1
Don’t Do Things You Can’t Undo: Reversibility Models for Generating Safe Behaviours
"... Abstract—We argue that an ability to determine the reversibility of actions allows a robot to identify safe behaviors autonomously. We introduce a notion of reversibility model and give a definition of model refinement. We implement this on a real robot and observe that, when a reversibility model i ..."
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Abstract—We argue that an ability to determine the reversibility of actions allows a robot to identify safe behaviors autonomously. We introduce a notion of reversibility model and give a definition of model refinement. We implement this on a real robot and observe that, when a reversibility model is refined by the addition of proximity sensors, obstacle avoidance emerges as a sideeffect of avoiding irreversible actions. We interpret this as evidence of a deep connection between reversibility and safe behaviour. We also observe that, on the real robot, reversiblities are learned as efficiently as a dedicated reward function. We conclude that reversibility identification may provide an abstract and yet practical method of generating a variety of safe behaviours.
A Universal Characterisation of the Closed Euclidean Interval
 in: Proceedings of 16th Annual IEEE Symposium on Logic in Computer Science
"... We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. We test the notion in categories of interest. In the category of sets, any closed and bounded interval of real numbers is an interval object. In the ca ..."
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Cited by 4 (3 self)
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We propose a notion of interval object in a category with finite products, providing a universal property for closed and bounded real line segments. We test the notion in categories of interest. In the category of sets, any closed and bounded interval of real numbers is an interval object. In the category of topological spaces, the interval objects are closed and bounded intervals with the Euclidean topology. We also prove that an interval object exists in any elementary topos with natural numbers object. The universal property of an interval object provides a mechanism for defining functions on the interval. We use this to define basic arithmetic operations, and to verify equations between them. It also allows us to develop an analogue of the primitive recursive functions, yielding a natural class of computable functions on the interval. Contents 1
A Linear Metainterpreter for the Situation Calculus
 Journal of Logic and Computation
"... This paper describes an application of the linear logic programming language Lygon ..."
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Cited by 3 (2 self)
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This paper describes an application of the linear logic programming language Lygon
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