Bounded LTL Model Checking with Stable Models

In this paper bounded model checking of asynchronous concurrent systems is introduced as a promising application area for answer set programming. As the model of asynchronous systems a generalisation of communicating automata, 1-safe Petri nets, are used. It is shown how a 1-safe Petri net and a requirement on the behaviour of the net can be translated into a logic program such that the bounded model checking problem for the net can be solved by computing stable models of the corresponding program. The use of the stable model semantics leads to compact encodings of bounded reachability and deadlock detection tasks as well as the more general problem of bounded model checking of linear temporal logic. Correctness proofs of the devised translations are given, and some experimental results using the translation and the Smodels system are presented.Comment: 32 pages, to appear in Theory and Practice of Logic Programmin

Cell-Degradation of Calcium Phosphate Ceramics

Calcium phosphate ceramics are used in bone surgery under different forms: dense or porous ceramic s as bone substitute, thin ceramic coatings on metallic implants as an osseointegration enhancer. Their degradation depends on their physico-chemical properties and particularly on their chemical composition. Natural calcium phosphates of bone are degraded by mononuclear or multinuclear cells and the extracellular matrix induces the differentiation of the degrading-cells. Hydroxyapatite, which is one of the most used calcium phosphates , is known as a low degradation material. However, the histological analysis of implanted HA-materials both in animals and in humans showed that a cellular degradation took place on the surface of the material

Hybrid Rules with Well-Founded Semantics

A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive negation for logic programs. Hybrid rules are normal clauses extended with constraints in the bodies; constraints are certain formulae in the language of the external theory. A hybrid program is a pair of a set of hybrid rules and an external theory. Instances of the framework are obtained by specifying the class of external theories, and the class of constraints. An example instance is integration of (non-disjunctive) Datalog with ontologies formalized as description logics. The paper defines a declarative semantics of hybrid programs and a goal-driven formal operational semantics. The latter can be seen as a generalization of SLS-resolution. It provides a basis for hybrid implementations combining Prolog with constraint solvers. Soundness of the operational semantics is proven. Sufficient conditions for decidability of the declarative semantics, and for completeness of the operational semantics are given

Generating Random Logic Programs Using Constraint Programming

Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs, experimental evaluations are limited to only a few programs. Existing methods to generate random logic programs are limited to propositional programs and often impose stringent syntactic restrictions. We present a novel approach to generating random logic programs and random probabilistic logic programs using constraint programming, introducing a new constraint to control the independence structure of the underlying probability distribution. We also provide a combinatorial argument for the correctness of the model, show how the model scales with parameter values, and use the model to compare probabilistic inference algorithms across a range of synthetic problems. Our model allows inference algorithm developers to evaluate and compare the algorithms across a wide range of instances, providing a detailed picture of their (comparative) strengths and weaknesses.Comment: This is an extended version of the paper published in CP 202

Relational grounding facilitates development of scientifically useful multiscale models

We review grounding issues that influence the scientific usefulness of any biomedical multiscale model (MSM). Groundings are the collection of units, dimensions, and/or objects to which a variable or model constituent refers. To date, models that primarily use continuous mathematics rely heavily on absolute grounding, whereas those that primarily use discrete software paradigms (e.g., object-oriented, agent-based, actor) typically employ relational grounding. We review grounding issues and identify strategies to address them. We maintain that grounding issues should be addressed at the start of any MSM project and should be reevaluated throughout the model development process. We make the following points. Grounding decisions influence model flexibility, adaptability, and thus reusability. Grounding choices should be influenced by measures, uncertainty, system information, and the nature of available validation data. Absolute grounding complicates the process of combining models to form larger models unless all are grounded absolutely. Relational grounding facilitates referent knowledge embodiment within computational mechanisms but requires separate model-to-referent mappings. Absolute grounding can simplify integration by forcing common units and, hence, a common integration target, but context change may require model reengineering. Relational grounding enables synthesis of large, composite (multi-module) models that can be robust to context changes. Because biological components have varying degrees of autonomy, corresponding components in MSMs need to do the same. Relational grounding facilitates achieving such autonomy. Biomimetic analogues designed to facilitate translational research and development must have long lifecycles. Exploring mechanisms of normal-to-disease transition requires model components that are grounded relationally. Multi-paradigm modeling requires both hyperspatial and relational grounding

Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks

<p>Abstract</p> <p>Background</p> <p>For large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.</p> <p>Results</p> <p>In this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.</p> <p>Conclusion</p> <p>In conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.</p

(Mathematical) Logic for Systems Biology (Invited Paper)

International audienceWe advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The potential candidate logics should have a traditional proof theoretic pedigree (including a sequent calculus presentation enjoying cut-elimination and focusing), and should come with (certified) proof tools. Beyond providing a reliable framework, this allows the adequate encodings of our biological systems. We present two candidate logics (two modal extensions of linear logic, called HyLL and SELL), along with biological examples. The examples we have considered so far are very simple ones-coming with completely formal (interactive) proofs in Coq. Future works includes using automatic provers, which would extend existing automatic provers for linear logic. This should enable us to specify and study more realistic examples in systems biology, biomedicine (diagnosis and prognosis), and eventually neuroscience