Declarative Semantics Research Articles

Declarative probabilistic logic programming in discrete-continuous domains

Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming languages owes much of its success to a declarative semantics, the so-called distribution semantics. However, the distribution semantics is limited to discrete random variables only. While PLP has been extended in various ways for supporting hybrid, that is, mixed discrete and continuous random variables, we are still lacking a declarative semantics for hybrid PLP that not only generalizes the distribution semantics and the modeling language but also the standard inference algorithm that is based on knowledge compilation. We contribute the measure semantics together with the hybrid PLP language DC-ProbLog (where DC stands for distributional clauses) and its inference engine infinitesimal algebraic likelihood weighting (IALW). These have the original distribution semantics, standard PLP languages such as ProbLog, and standard inference engines for PLP based on knowledge compilation as special cases. Thus, we generalize the state of the art of PLP towards hybrid PLP in three different aspects: semantics, language and inference. Furthermore, IALW is the first inference algorithm for hybrid probabilistic programming based on knowledge compilation.

Incremental Event Calculus for Run-Time Reasoning

We present a system for online, incremental composite event recognition. In streaming environments, the usual case is for data to arrive with a (variable) delay from, and to be revised by, the underlying sources. We propose RTECinc, an incremental version of RTEC, a composite event recognition engine with formal, declarative semantics, that has been shown to scale to several real-world data streams. RTEC deals with delayed arrival and revision of events by computing all queries from scratch. This is often inefficient since it results in redundant computations. Instead, RTECinc deals with delays and revisions in a more efficient way, by updating only the affected queries. We examine RTECinc theoretically, presenting a complexity analysis, and show the conditions in which it outperforms RTEC. Moreover, we compare RTECinc and RTEC experimentally using real-world and synthetic datasets. The results are compatible with our theoretical analysis and show that RTECinc outperforms RTEC in many practical cases.

Semantic data management in P2P systems driven by self-esteem

Abstract This paper is a contribution to semantic data management in P2P systems. It is based on the previous works of the same authors in which a declarative semantics for P2P systems is defined: under this semantics, only facts not making the local databases inconsistent are imported (Weak Models) and the Maximal Weak Models are those in which peers import maximal sets of facts not violating integrity constraints. The proposal, presented in this paper, stems from the following two observations: (i) the Maximal Weak Model Semantics ensures that locally consistent P2P systems always admit a maximal weak model, but fails for locally inconsistent P2P systems; (ii) the self-esteem degree of a peer should impact on the interaction with other peers in the system so that driving the integration process. From the above-mentioned observations a more general framework is presented. Our proposal is able to manage local inconsistencies and allows to model a peer integration process driven by the self-esteem degree of each peer. Different self-esteem degrees could be considered; in this paper we focus our attention on three different scenarios in which a generic peer can declare an high, low or medium self-esteem degree, stating respectively that it trusts its own knowledge more, less or equally with respect to the knowledge that can be provided from the rest of the system. Three different basic semantics are proposed, High, Low, Medium Self-Esteem Semantics and results about the computational complexity of P2P logic queries are investigated by considering brave and cautions reasoning. The paper also presents an extension of the basic framework of the Self-Esteem Semantics that models a finer-grained self-esteem concept and allows each peer to exhibit different levels of self-esteem each of them defined with respect to a subset of its mapping rules.

Dischargeable Obligations in the 𝒮CIFF Framework

Abductive Logic Programming (ALP) has been proven very effective for formalizing societies of agents, commitments and norms, in particular by mapping the most common deontic operators (obligation, prohibition, permission) to abductive expectations. In our previous works, we have shown that ALP is a suitable framework for representing norms. Normative reasoning and query answering were accommodated by the same abductive proof procedure, named 𝒮CIFF. In this work, we introduce a defeasible flavour in this framework, in order to possibly discharge obligations in some scenarios. Abductive expectations can also be qualified as dischargeable, in the new, extended syntax. Both declarative and operational semantics are improved accordingly, and proof of soundness is given under syntax allowedness conditions Moreover, the dischargement itself might be proved invalid, or incoherent with the rules, due to new knowledge provided later on. In such a case, a discharged expectation might be reinstated and hold again after some evidence is given. We extend the notion of dischargement to take into consideration also the reinstatement of expectations. The expressiveness and power of the extended framework, named 𝒮CIFF𝒟, is shown by modeling and reasoning upon a fragment of the Japanese Civil Code. In particular, we consider a case study concerning manifestations of intention and their rescission (Section II of the Japanese Civil Code).

Flexible coinductive logic programming

AbstractRecursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations, necessary in some cases to get the correct meaning. We provide a detailed formal account of an extension of logic programming supporting flexible coinduction. Syntactically, programs are enriched by coclauses, clauses with a special meaning used to tune the interpretation of predicates. As usual, the declarative semantics can be expressed as a fixed point which, however, is not necessarily the least, nor the greatest one, but is determined by the coclauses. Correspondingly, the operational semantics is a combination of standard SLD resolution and coSLD resolution. We prove that the operational semantics is sound and complete with respect to declarative semantics restricted to finite comodels.

Probabilistic reasoning about epistemic action narratives

We propose the action language EPEC – Epistemic Probabilistic Event Calculus – that supports probabilistic, epistemic reasoning about narratives of action occurrences and environmentally triggered events, and in particular facilitates reasoning about future belief-conditioned actions and their consequences in domains that include both perfect and imperfect sensing actions. To provide a declarative semantics for sensing and belief conditioned actions in a probabilistic, narrative setting we introduce the novel concept of an epistemic reduct. We then formally compare our language with two established frameworks for probabilistic reasoning about action – the action language PAL by Baral et al., and the extension of the situation calculus to reason about noisy sensors and effectors by Bacchus et al. In both cases we prove a correspondence with EPEC for a class of domains representable in both frameworks.

Revisiting Object-Rule Fusion in Query Languages

Abstract Object-oriented (O2) and declarative rule-based (RB) paradigms are known and intensively used for decades. There have been many approaches to combine O2 and RB concepts in a uniform framework. However, they either focus on embedding rules into O2 languages, or provide a declarative semantics and proof theory for the O2 machinery. In the current paper we focus on understanding objects as basic building blocks for deductive queries. To achieve the goal of object-rule fusion we use carefully chosen elementary constructs, encompassed in a simple and uniform framework easily extendable and adaptable to many existing RB languages.

A Logic Framework for P2P Deductive Databases

AbstractThis paper presents a logic framework for modeling the interaction among deductive databases in a peer-to-peer (P2P) environment. Each peer joining a P2P systemprovides or imports datafrom its neighbors by using a set ofmapping rules, that is, a set of semantic correspondences to a set of peers belonging to the same environment. By using mapping rules, as soon as it enters the system, a peer can participate and access all data available in its neighborhood, and through its neighborhood it becomes accessible to all the other peers in the system. A query can be posed to any peer in the system and the answer is computed by using locally stored data and all the information that can be consistently imported from the neighborhood. Two different types of mapping rules are defined: mapping rules allowing to import a maximal set of atoms not leading to inconsistency (calledmaximal mapping rules) and mapping rules allowing to import a minimal set of atoms needed to restore consistency (calledminimal mapping rules). Implicitly, the use of maximal mapping rules statesit is preferable to import as long as no inconsistencies arise; whereas the use of minimal mapping rules states thatit is preferable not to import unless a inconsistency exists. The paper presents three different declarative semantics of a P2P system: (i) theMax Weak Model Semantics, in which mapping rules are used to importas much knowledge as possiblefrom a peer’s neighborhood without violating local integrity constraints; (ii) theMin Weak Model Semantics, in which the P2P system can be locally inconsistent and the information provided by the neighbors is used to restore consistency, that is, to only integrate the missing portion of a correct, but incomplete database; (iii) theMax-Min Weak Model Semanticsthat unifies the previous two different perspectives captured by the Max Weak Model Semantics and Min Weak Model Semantics. This last semantics allows to characterize each peer in the neighborhood as a resource used either to enrich (integrate) or to fix (repair) the knowledge, so as to define a kind ofintegrate–repairstrategy for each peer. For each semantics, the paper also introduces an equivalent and alternative characterization, obtained by rewriting each mapping rule into prioritized rules so as to model a P2P system as a prioritized logic program. Finally, results about the computational complexity of P2P logic queries are investigated by consideringbraveandcautiousreasoning.

LARS: A Logic-based framework for Analytic Reasoning over Streams

The increasing availability of streaming data has accelerated advances in information processing tools that no longer store data for static querying but push information to consumers as soon as it becomes available. Stream processing aims at providing languages and tools for data that changes at a high rate. To cope with the volume of data, query languages often extend existing approaches for static data by means of window operators that return snapshots of recent data. However, the semantics of these languages are often given only informally or operationally, which makes their analysis and comparison difficult. A formal means to express the declarative semantics of such systems seems to be missing. This lack of theory is of particular relevance for the emerging research in stream reasoning which shifts the focus from throughput to higher expressiveness. To fill this gap, we present LARS, a Logic-based framework for Analytic Reasoning over Streams. At its core, LARS formulas extend propositional logic with generic window operators and additional controls to handle temporal information. On top of this, LARS programs extend Answer Set Programming (ASP) with rich stream reasoning capabilities; the latter can be exploited to target AI applications in a streaming context, such as diagnosis, configuration or planning. Specifically, we study in this article the computational complexity of LARS formulas and programs, their relationship to Linear Temporal Logic (LTL) and the well-known Continuous Query Language (CQL). Furthermore, we discuss the modeling capabilities of LARS in notes on the SPARQL extensions C-SPARQL and CQELS, and on the interval-based approach of the complex event processing language ETALIS. We finally briefly touch available implementations, in particular, the recent prototype engines Laser and Ticker that aim for high throughput and high expressiveness, respectively. Notably, both engines specify their semantics in LARS, indicating the desired flexibility of the framework and its potential as stream reasoning language itself, which is further explored in other works.

Stream Reasoning with LARS

Stream reasoning is the task of continuously deriving conclusions on streaming data. Different research communities emphasize different aspects such as throughput vs. expressiveness, yet a mathematical model to describe the declarative semantics of such systems has been missing. This motivated the logic-based framework LARS for analytic reasoning over streams. However, it is also attractive for applications by itself.

Thresholded semantic framework for a fully integrated fuzzy logic language

This work proposes a declarative semantics based on a fuzzy variant of the classical notion of least Herbrand model for the so-called FASILL programming language (acronym of “Fuzzy Aggregators and Similarity Into a Logic Language”) which has been recently designed and implemented for coping with implicit/explicit truth degree annotations, a great variety of connectives and unification by similarity. Also, we define an immediate consequence operator that allows us to give a fixpoint characterization of the least Herbrand model for a FASILL program. A remarkable aspect of our declarative and fixpoint semantics is the fact that both have been enriched with the use of thresholds thanks to the natural ability of the underlying fuzzy language for managing such constructs. Moreover, we have connected both semantics with an operational one, which also manages thresholds in an efficient way, by proving the correctness of the whole semantic framework.

Extending Coinductive Logic Programming with Co-Facts

We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic programming, interpretations are subsets of the complete Herbrand basis, including infinite terms. However, the intended meaning (declarative semantics) of a program is a fixed point which is not necessarily the least, nor the greatest one, but is determined by co-facts. In this way, it is possible to express predicates on non well-founded structures, such as infinite lists and graphs, for which the coinductive interpretation would be not precise enough. Moreover, this paradigm nicely subsumes standard (inductive) and coinductive logic programming, since both can be expressed by a particular choice of co-facts, hence inductive and coinductive predicates can coexist in the same program. We illustrate the paradigm by examples, and provide declarative and operational semantics, proving the correctness of the latter. Finally, we describe a prototype meta-interpreter.

On concurrent behaviors and focusing in linear logic

Concurrent Constraint Programming (CCP) is a simple and powerful model of concurrency where processes interact by telling and asking constraints into a global store of partial information. Since its inception, CCP has been endowed with declarative semantics where processes are interpreted as formulas in a given logic. This allows for the use of logical machinery to reason about the behavior of programs and to prove properties of them. Nevertheless, the logical characterization of CCP programs exhibits normally a weak level of adequacy since proofs in the logical system may not correspond directly to traces of the program. In this paper, we study different encodings from CCP into intuitionistic linear logic (ILL) and we compare the level of adequacy attained in each. By relying on a focusing discipline, we show that it is possible to give a logical characterization to CCP with the highest level of adequacy. Moreover, we show how to characterize maximal-parallelism semantics for CCP by relying on a multi-focusing discipline for ILL. These results, besides giving proof techniques for CCP, entail (safe) optimizations for the execution of CCP programs. Finally, we show how to interpret CCP procedure calls as fixed points in ILL, thus opening the possibility of reasoning by induction about properties of CCP programs.

On scaling dynamic programming problems with a multithreaded tabling Prolog system

Prolog system scaling the execution of dynamic programming problems.New design supporting multithreaded tabling in Prolog systemsApplication of multithreaded tabling to well-known dynamic programming problems.Experimental results showing promising speedup results up to 32 cores. Tabling is a powerful implementation technique that improves the declarativeness and expressiveness of traditional Prolog systems in dealing with recursion and redundant computations. It can be viewed as a natural tool to implement dynamic programming problems, where a general recursive strategy divides a problem in simple sub-problems that are often the same. When tabling is combined with multithreading, we have the best of both worlds, since we can exploit the combination of higher declarative semantics with higher procedural control. However, at the engine level, such combination for dynamic programming problems is very difficult to exploit in order to achieve execution scalability as we increase the number of running threads. In this work, we focus on two well-known dynamic programming problems, the Knapsack and the Longest Common Subsequence problems, and we discuss how we were able to scale their execution by using the multithreaded tabling engine of the Yap Prolog system. To the best of our knowledge, this is the first work showing a Prolog system to be able to scale the execution of multithreaded dynamic programming problems. Our experiments also show that our system can achieve comparable or even better speedup results than other parallel implementations of the same problems.

Declarative semantics of transactions in ORM

In order to specify databases completely at the conceptual level, conceptual database specification languages should contain a data definition (sub)language (DDL), for specifying data structures (+constraints), a data retrieval (sub)language (DRL), for specifying queries, as well as a (declarative) data manipulation (sub)language (DML), for specifying transactions.Object Role Modeling (ORM) is a powerful method for designing and querying database models at the conceptual level. By means of verbalization the application is also described in natural language as used by domain experts, for communication and validation purposes. ORM currently comprises a DDL and a DRL (ConQuer). However, the ORM-method does not yet contain an expressive DML for specifying transactions at the conceptual level.In an earlier paper we designed a syntactic extension of the ORM-method with a DML for specifying transactions at the conceptual level in a purely declarative way. For all transactions we proposed syntaxes, verbalizations, and diagrams. However, we did not give a formal semantics then.The purpose of this paper is to add a clear, formal and purely declarative semantics to the proposed ORM-transactions. The paper also formally defines rollbacks and illustrates everything with examples (including a solution to a well-known transaction specification problem). The extension of ORM with an expressive set of completely declaratively specified transactions makes ORM complete as a database specification method at the conceptual level.

An event calculus production rule system for reasoning in dynamic and uncertain domains

AbstractAction languages have emerged as an important field of knowledge representation for reasoning about change and causality in dynamic domains. This paper presents Cerbere, a production system designed to perform online causal, temporal and epistemic reasoning based on the Event Calculus. The framework implements the declarative semantics of the underlying logic theories in a forward-chaining rule-based reasoning system, coupling the high expressiveness of its formalisms with the efficiency of rule-based systems. To illustrate its applicability, we present both the modeling of benchmark problems in the field, as well as its utilization in the challenging domain of smart spaces. A hybrid framework that combines logic-based with probabilistic reasoning has been developed, that aims to accommodate activity recognition and monitoring tasks in smart spaces.

Declaratively building behavior by means of scenario clauses

Behavior needs to be understood from early stages of software development. In this context, incremental and declarative modeling seems an attractive approach for closely capturing and analyzing requirements without early operational commitment. A traditional choice for such a kind of modeling is a logic-based approach. Unfortunately, in many cases, the formal description and validation of properties result in a daunting task, even for trained people. Moreover, some authors established some practical limitations with temporal logics expressive power. In this work, we present omega-feather weight visual scenarios ($$\omega$$ź-FVS) a declarative language, not founded on temporal logics, but on simple graphical scenarios, powerful enough to express $$\omega$$ź-regular properties. The notation is equipped with declarative semantics based on morphisms, and a tableau procedure is given enabling the possibility of automatic analysis.

Verification of Spatial and Temporal Modalities in Biochemical Systems

Biochemical systems such as metabolic and signaling pathways tend to be arranged in a physical space: the product of one reaction must be in the right place to become the reactant for the subsequent reaction in the pathway. Moreover, in some cases, the behavior of the systems can depend on both, the location of the reactants as well as on the time needed for the reaction to occur. We address the problem of specifying and verifying properties of biochemical systems that exhibit both temporal and spatial modalities at the same time. For that, we use as specification language a fragment of intuitionistic linear logic with subexponentials (SELL). The subexponential signature allows us to capture the spatial relations among the different components of the system and the timed constraints for reactions to occur. We show that our framework is general enough to give a declarative semantics to P-Systems and we show that such logical characterization has a strong level of adequacy. Hence, derivations in SELL follow exactly the behavior of the modeled system.

Putting logic-based distributed systems on stable grounds

AbstractIn the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has been lacking so far. The challenge is to capture precisely the amount of nondeterminism that is inherent to distributed computations due to concurrency, networking delays, and asynchronous communication. This paper shows how a declarative, model-based semantics can be obtained by simply using the well-known stable model semantics for Datalog with negation. We show that the model-based semantics matches previously proposed formal operational semantics.

PTL: A model transformation language based on logic programming

In this paper we present a model transformation language based on logic programming. The language, called PTL (Prolog based Transformation Language), can be considered as a hybrid language in which ATL (Atlas Transformation Language)-style rules are combined with logic rules for defining transformations. ATL-style rules are used to define mappings from source models to target models while logic rules are used as helpers. The implementation of PTL is based on the encoding of the ATL-style rules by Prolog rules. Thus, PTL makes use of Prolog as a transformation engine. We have provided a declarative semantics to PTL and proved the semantics equivalent to the encoded program. We have studied an encoding of OCL (Object Constraint Language) with Prolog goals in order to map ATL to PTL. Thus a subset of PTL can be considered equivalent to a subset of ATL. The proposed language can be also used for model validation, that is, for checking constraints on models and transformations. We have equipped our language with debugging and tracing capabilities which help developers to detect programming errors in PTL rules. Additionally, we have developed an Eclipse plugin for editing PTL programs, as well as for debugging, tracing and validation. Finally, we have evaluated the language with several transformation examples as well as tested the performance with large models.