Generating Schemata of Resolution Proofs

Two distinct algorithms are presented to extract (schemata of) resolution proofs from closed tableaux for propositional schemata. The first one handles the most efficient version of the tableau calculus but generates very complex derivations (denoted by rather elaborate rewrite systems). The second one has the advantage that much simpler systems can be obtained, however the considered proof procedure is less efficient

A Dynamic Macroeconomic Model for the US Telecommunications Industry

Dynamic models have been used in most businesses serving different purposes. The increased changes of the Telecommunications environment have created a dynamic industry emerging new dynamic economic models. We investigated the Telecom industry by conducting macroeconomic and infrastructure analysis. However, this paper uses recent data from the Telecommunications industry to reveal the infrastructure trends and predict the US wireless growth. The analysis is focused on several factors such as the infrastructure described by the Teledensity, the employment and the Telecom revenues in comparison with the Gross Domestic Product (GDP). The purpose of this analysis is to understand the industry’s behavior during a specific period of time, 1984-2003, propose an appropriate economic dynamic model, wireless oriented that identifies the current driving forces and detects the impact of some critical events and trends.Dynamic Economic Model, Macroeconomic Analysis, Telecom Act, Teledensity

Integrating a Global Induction Mechanism into a Sequent Calculus

Most interesting proofs in mathematics contain an inductive argument which requires an extension of the LK-calculus to formalize. The most commonly used calculi for induction contain a separate rule or axiom which reduces the valid proof theoretic properties of the calculus. To the best of our knowledge, there are no such calculi which allow cut-elimination to a normal form with the subformula property, i.e. every formula occurring in the proof is a subformula of the end sequent. Proof schemata are a variant of LK-proofs able to simulate induction by linking proofs together. There exists a schematic normal form which has comparable proof theoretic behaviour to normal forms with the subformula property. However, a calculus for the construction of proof schemata does not exist. In this paper, we introduce a calculus for proof schemata and prove soundness and completeness with respect to a fragment of the inductive arguments formalizable in Peano arithmetic.Comment: 16 page

From Specifications to Behavior: Maneuver Verification in a Semantic State Space

To realize a market entry of autonomous vehicles in the foreseeable future, the behavior planning system will need to abide by the same rules that humans follow. Product liability cannot be enforced without a proper solution to the approval trap. In this paper, we define a semantic abstraction of the continuous space and formalize traffic rules in linear temporal logic (LTL). Sequences in the semantic state space represent maneuvers a high-level planner could choose to execute. We check these maneuvers against the formalized traffic rules using runtime verification. By using the standard model checker NuSMV, we demonstrate the effectiveness of our approach and provide runtime properties for the maneuver verification. We show that high-level behavior can be verified in a semantic state space to fulfill a set of formalized rules, which could serve as a step towards safety of the intended functionality.Comment: Published at IEEE Intelligent Vehicles Symposium (IV), 201

Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one logic to the other. Some consequences about complexity are given. We report about first experiments and the consequences about possible improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs, additional examples & figures, additional comparison between classical LTL/schemata algorithms up to the provided translations, and an example of how to do model checking with schemata; 36 pages, 8 figure

A Decidable Class of Nested Iterated Schemata (extended version)

Many problems can be specified by patterns of propositional formulae depending on a parameter, e.g. the specification of a circuit usually depends on the number of bits of its input. We define a logic whose formulae, called "iterated schemata", allow to express such patterns. Schemata extend propositional logic with indexed propositions, e.g. P_i, P_i+1, P_1, and with generalized connectives, e.g. /\i=1..n or i=1..n (called "iterations") where n is an (unbound) integer variable called a "parameter". The expressive power of iterated schemata is strictly greater than propositional logic: it is even out of the scope of first-order logic. We define a proof procedure, called DPLL*, that can prove that a schema is satisfiable for at least one value of its parameter, in the spirit of the DPLL procedure. However the converse problem, i.e. proving that a schema is unsatisfiable for every value of the parameter, is undecidable so DPLL* does not terminate in general. Still, we prove that it terminates for schemata of a syntactic subclass called "regularly nested". This is the first non trivial class for which DPLL* is proved to terminate. Furthermore the class of regularly nested schemata is the first decidable class to allow nesting of iterations, i.e. to allow schemata of the form /\i=1..n (/\j=1..n ...).Comment: 43 pages, extended version of "A Decidable Class of Nested Iterated Schemata", submitted to IJCAR 200

Schemata of SMT problems

Session 3 (full paper)International audienceA logic is devised for reasoning about iterated schemata of SMT problems. The satisfiability problem is shown to be undecidable for this logic, but we present a proof procedure that is sound, complete w.r.t. satisfiability and terminating for a precisely characterized class of problems. It is parameterized by an external procedure (used as a black box) for testing the satisfiability of ground instances of the schema in the considered theory (e.g. integers, reals etc.)

Bevacizumab in combination with chemotherapy for the treatment of advanced ovarian cancer: a systematic review

As increased angiogenesis has been linked with the progression of ovarian cancer, a number of anti-angiogenic agents have been investigated, or are currently in development, as potential treatment options for patients with advanced disease. Bevacizumab, a recombinant monoclonal antibody against vascular endothelial growth factor, has gained European Medicines Agency approval for the front-line treatment of advanced epithelial ovarian cancer, fallopian tube cancer or primary peritoneal cancer in combination with carboplatin and paclitaxel, and for the treatment of first recurrence of platinum-sensitive ovarian cancer in combination with carboplatin and gemcitabine. We conducted a systematic literature review to identify available efficacy and safety data for bevacizumab in ovarian cancer as well as for newer anti-angiogenic agents in development. We analyzed published data from randomized, controlled phase II/III clinical trials enrolling women with ovarian cancer to receive treatment with bevacizumab. We also reviewed available data for emerging anti-angiogenic agents currently in phase II/III development, including trebananib, aflibercept, nintedanib, cediranib, imatinib, pazopanib, sorafenib and sunitinib. Significant efficacy gains were achieved with the addition of bevacizumab to standard chemotherapy in four randomized, double-blind, phase III trials, both as front-line treatment (GOG-0218 and ICON7) and in patients with recurrent disease (OCEANS and AURELIA). The type and frequency of bevacizumab-related adverse events was as expected in these studies based on published data. Promising efficacy data have been published for a number of emerging anti-angiogenic agents in phase III development for advanced ovarian cancer. Further research is needed to identify predictive or prognostic markers of response to bevacizumab in order to optimize patient selection and treatment benefit. Data from phase III trials of newer anti-angiogenic agents in ovarian cancer are awaited