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An Interactive Semantics of Logic Programming
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We apply to logic programming some recently emerging ideas from the field of reductionbased communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we ..."
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Cited by 8 (6 self)
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We apply to logic programming some recently emerging ideas from the field of reductionbased communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.
Open Ended Systems, Dynamic Bisimulation and Tile Logic
, 2000
"... The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence pro ..."
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The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence property with such axioms and with the specication of open ended systems, where states can be recongured at runtime, at the cost of an innitary operation at the metalevel. We show that the compositional framework oered by tile logic is suitable to deal with structural axioms and open ended systems specications, allowing for a nitary presentation of context closure. Keywords: Bisimulation, sos formats, dynamic bisimulation, tile logic. Introduction The semantics of dynamic systems can be conveniently expressed via labelled transition systems (lts) whose states are terms over a certain algebra and whose labels describe some abstract behavioral information. Provided such informatio...
Implementing Tile Systems: Some Examples From Process Calculi
, 1998
"... this paper we show some example of their application to implement concurrent process calculi. In particular, in Section 2 we define executable implementations of CCSlike languages, preserving their original operational semantics. The two case studies considered here are the tile specification of fi ..."
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Cited by 6 (4 self)
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this paper we show some example of their application to implement concurrent process calculi. In particular, in Section 2 we define executable implementations of CCSlike languages, preserving their original operational semantics. The two case studies considered here are the tile specification of finite CCS given in
Symmetric and Cartesian Double Categories as a Semantic Framework for Tile Logic
, 1995
"... this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for eff ..."
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Cited by 6 (5 self)
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this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for effects, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four
Normal Forms for Algebras of Connections
 Theoretical Computer Science
, 2000
"... Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, ..."
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Cited by 5 (4 self)
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Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, but an exhaustive comparison between them is sometimes difficult, because their presentations can be quite dissimilar. This work is a first step towards a unified view: Focusing on the primitive ingredients of distributed spaces (namely interfaces, links and basic modules), we introduce a general schema for describing a normal form presentation of many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable monoidal categories.
Tile Transition Systems as Structured Coalgebras
 FUNDAMENTALS OF COMPUTATION THEORY, VOLUME 1684 OF LNCS
, 1999
"... The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as ..."
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The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting. In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. However, structured coalgebras are more restrictive than tile models. Those models which can be presented as st...
Logical Specification of Operational Semantics
 IN CSL'99, PROC. CONF. ON COMPUTER SCIENCE LOGIC, VOLUME 1683 OF LNCS
, 1999
"... Various logicbased frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts ..."
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Various logicbased frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts, rewriting logic, and tile logic. We consider
2003b, ‘Category Theory and Higher Dimensional Algebra: Potential Descriptive Tools in Neuroscience
 Proceedings of the International Conference on Theoretical Neurobiology, Delhi, February 2003, National Brain Research Centre, Conference Proceedings
"... We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes. ..."
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Cited by 3 (1 self)
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We explain the notion of colimit in category theory as a potential tool for describing structures and their communication, and the notion of higher dimensional algebra as potential yoga for dealing with processes and processes of processes.
Comparing HigherOrder Encodings in Logical Frameworks and Tile Logic
, 2001
"... In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tr ..."
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In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tracing di#erences and analogies on the basis of two case studies: late #calculus and lazy simply typed #calculus.