Maria Chiara Meo

A timed concurrent constraint language

Abstract We study a timed concurrent constraint language, called tccp , which is obtained by a natural timed interpretation of the usual ccp constructs: action-prefixing is interpreted as the next-time operator and the parallel execution of agents follows the scheduling policy of maximal parallelism. Additionally, tccp includes a simple primitive which allows one to specify timing constraints. We define the operational semantics of tccp by means of a transition system and we define a denotational model which is fully abstract with respect to the usual notion of observables (that is, the results of terminating computations). Moreover, we study the semantics and expressive power of the notion of maximal parallelism underlying the computational model of tccp : We define a fully abstract semantics for a sublanguage of tccp , called ccpm , which essentially is concurrent constraint programming, provided that we interpret the parallel operator in terms of maximal parallelism rather than of interleaving. We show that tccp is strictly more expressive than ccpm which, in its turn, is strictly more expressive than ccp .

A compositional semantics for logic programs

Bossi, A., M. Gabbrielli, G. Levi and M.C. Meo, A compositional semantics for logic programs, Theoretical Computer Science 122 (1994) 3-47. This paper considers open logic programs originally introduced as a tool to build an OR-compositional semantics of logic programs. We extend the original semantic definitions in the framework of the general approach to the semantics,of logic programs described by Gabbrielli and Levi (1991). We first define an operational semantic

A Theory of Observables for Logic Programs

Lno6P) which models computed answer substitutions and which is compositional w.r.t. the union 6f programs. Next, we consider the semantic domain of Q-denotations, which are sets of clauses with a suitable equivalence relation. The fixpoint semantics F;(P) given by Bossi and Menegus (1991) is proved equivalent to the operational semantics. From the model-theoretic viewpoint, an Q-denotation is mapped onto a set of Herbrand interpretations, thus leading to a definition of an R-model based on the classical notion of truth. Moreower, we consider a particular kind of Q-models (compositional modelsL and we show that I”,(P) is a (nonminimal) compositional Q-model. A suitable abstraction oq0,( P) is compositional and fully

Proving Properties of Logic Programs by Abstract Diagnosis

We define a semantic framework to reason about properties of abstractions of SLD-derivations. The framework allows us to address problems such as the relation between the (top-down) operational semantics and the (bottom-up) denotational semantics, the existence of a denotation for a set of definite clauses and their properties (compositionality w.r.t. various syntactic operators, correctness, minimality, and precision). Using abstract interpretation techniques to model abstraction allows us to state very simple conditions on the observables which guarantee the validity of several general theorems.

Transformations of CCP programs

We show how declarative diagnosis techniques can be extended to cope with verification of operational properties, such as computed answers, and of abstract properties, such as types and groundness dependencies. The extension is achieved by using a simple semantic framework, based on abstract interpretation. The resulting technique (abstract diagnosis) leads to elegant bottom-up and top-down verification methods, which do not require to determine the symptoms in advance, and which are effective in the case of abstract properties described by finite domains.

Compilative Constructive Negation in Constraint Logic Programs

We introduce a transformation system for concurrent constraint programming (CCP). We define suitable applicability conditions for the transformations that guarantee the input/output CCP semantics is also preserved when distinguishing deadlocked computations from successful ones and when considering intermediate results of (possibly) nonterminating computations.The system allows us to optimize CCP programs while preserving their intended meaning: In addition to the usual benefits for sequential declarative languages, the transformation of concurrent programs can also lead to the elimination of communication channels and of synchronization points, to the transformation of nondeterministic computations into deterministic ones, and to the crucial saving of computational space. Furthermore, since the transformation system preserves the deadlock behavior of programs, it can be used for proving deadlock-freeness of a given program with respect to a class of queries. To this aim, it is sometimes sufficient to apply our transformations and to specialize the resulting program with respect to the given queries in such a way that the obtained program is trivially deadlock-free.

Fixpoint Semantics for Partial Computed Answer Substitutions and Call Patterns

In this paper we define a new compilative version of constructive negation (intensional negation) in CLP and we prove its (non-ground) correctness and completeness wrt the 3-valued completion. We show that intensional negation is essentially equivalent to constructive negation and that it is indeed more efficient, as one would expect from the fact that it is a compilative technique, with the transformation and the associated normalization process being performed once and for all on the source program. We define several formal non-ground semantics, based either on the derivation rule or on the least fixpoint of an immediate consequence operator. All these semantics are proved to correctly model the observable behavior, from the viewpoint of answer constraints. We give some equivalence theorems and we show that all our denotations are the non-ground representation of a single partial interpretation, which is Φ P ↑ ω, where Φ P is the Fittings operator [12].

Observable Behaviors and Equivalences of Logic Programs

In this paper we study a declarative (fixpoint) semantics for logic programs which correctly models several kinds of partial answers and call patterns. We first show how the Ω-semantics [5,4] can model these observables when the selection rule is not taken into account. We then define a suitable immediate consequence operator, and hence a fixpoint semantics, for partial answers and call patterns which considers also the selection rule. Each observable induces an observational equivalence on programs. The semantics are then related to the observational equivalences by investigating correctness and full abstraction properties.

Resultants Semantics for Prolog

We first introduce a general semantic scheme for logic programs which provides a uniform framework for defining different compositional semantics parametrically with respect to a given notion of observability. The equivalence of the operational (top-down) and fixpoint (bottom-up) construction of the semantics is ensured by the scheme (provided a congruence property is verified). We then define several observational equivalences on logic programs and investigate how they are related. The equivalences are based on various observables (successful derivations, computed answers, partial computed answers and call patterns) and on a notion of program composition. For each observational equivalence we study the relation with a suitable formal semantics by investigating correctness and full abstraction properties. All the semantics we consider are obtained as instances of the general scheme.

Timed soft concurrent constraint programs

In this paper we study some rst order formulas, called resultants, which can be used to describe in a concise way most of the relevant information associated to SLD-derivations. We rst extend to resultants some classical results of logic programming theory. Then we deene a xpoint semantics for Prolog computed resultants, i.e. those formulas which are obtained by considering the leftmost selection rule. Suitable abstractions of such a semantics are then used to model call patterns and partial answers. Finally we show how these results can be generalized to a larger class of selection rules.