Using constrained intuitionistic linear logic for hybrid robotic planning problems

Synthesis of robot behaviors towards nontrivial goals often requires reasoning about both discrete and continuous aspects of the underlying domain. Existing approaches in building automated tools for such synthesis problems attempt to augment methods from either discrete planning or continuous control with hybrid elements, but largely fail to ensure a uniform treatment of both aspects of the domain. In this paper, we present a new formalism, Constrained Intuitionistic Linear Logic (CILL), merging continuous constraint solvers with linear logic to yield a single language in which hybrid properties of robotic behaviors can be expressed and reasoned with. Following a gentle introduction to linear logic, we describe the two new connectives of CILL, introduced to interface the constraint domain with the logical fragment of the language. We then illustrate the application of CILL for robotic planning problems within the Balanced Blocks World, a "physically realistic" extension of the Blocks World domain. Even though some of the formal proofs for the semantic foundations of the language as well as an efficient implementation of a theorem prover are yet to be completed, CILL promises to be a powerful formalism in reasoning within hybrid domains. © 2007 IEEE

Experiments in integrating constraints with logical reasoning for robotic planning within the twelf logical framework and the prolog language

Ankara : The Department of Computer Engineering and the Institute of Engineering and Sciences of Bilkent University, 2008.Thesis (Master's) -- Bilkent University, 2008.Includes bibliographical references leaves 92-96.The underlying domain of various application areas, especially real-time systems and robotic applications, generally includes a combination of both discrete and continuous properties. In robotic applications, a large amount of different approaches are introduced to solve either a discrete planning or control theoretic problem. Only a few methods exist to solve the combination of them. Moreover, these methods fail to ensure a uniform treatment of both aspects of the domain. Therefore, there is need for a uniform framework to represent and solve such problems. A new formalism, the Constrained Intuitionistic Linear Logic (CILL), combines continuous constraint solvers with linear logic. Linear logic has a great property to handle hypotheses as resources, easily solving state transition problems. On the other hand, constraint solvers deal well with continuous problems defined as constraints. Both properties of CILL gives us powerful ways to express and reason about the robotics domain. In this thesis, we focus on the implementation of CILL in both the Twelf Logical Framework and Prolog. The reader of this thesis can find answers of why classical aspects are not proper for the robotics domain, what advantages one can gain from intuitionism and linearity, how one can define a simple robotic domain in a logical formalism, how a proof in logical system corresponds to a plan in the robotic domain, what the advantages and disadvantages of logical frameworks and Prolog have and how the implementation of CILL can or cannot be done using both Twelf Logical Framework and Prolog.Duatepe, MertM.S

A backwards theorem prover with focusing, resource management and constraints for robotic planning within intuitionistic linear logic

Ankara : The Department of Computer Engineering and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 74-77.The main scope of this thesis is implementing a backwards theorem prover with focusing, resource management and constraints within the intuitionistic first-order linear logic for robotic planning problems. To this end, backwards formulations provide a simpler context for experimentation. However, existing backward theorem provers are either implemented without regard to the efficiency of the proofsearch, or when they do, restrict the language to smaller fragments such as Linear Hereditary Harrop Formulas (LHHF). The former approach is unsuitable since it significantly impairs the scalability of the resulting system. The latter family of theorem provers address the scalability issue but impact the expressivity of the resulting language and may not be able to deal with certain non-deterministic planning elements. The proof theory we describe in this thesis enables us to effectively experiment with the use of linearity and continuous constraints to encode dynamic state elements characteristic of robotic planning problems. To this end, we describe a prototype implementation of our system in SWI-Prolog, and also incorporate continuous constraints into the prototype implementation of the system. We support the expressivity and efficiency of our system with some examples.Kortik, SıtarM.S

A Constrained, Possibilistic Logical Approach for Software System Survivability Evaluation

In this paper, we present a logical framework to facilitate users in assessing a software system in terms of the required survivability features. Survivability evaluation is essential in linking foreign software components to an existing system or obtaining software systems from external sources. It is important to make sure that any foreign components/systems will not compromise the current system’s survivability properties. Given the increasing large scope and complexity of modern software systems, there is a need for an evaluation framework to accommodate uncertain, vague, or even ill-known knowledge for a robust evaluation based on multi-dimensional criteria. Our framework incorporates user-defined constrains on survivability requirements. Necessity-based possibilistic uncertainty and user survivability requirement constraints are effectively linked to logic reasoning. A proof-of-concept system has been developed to validate the proposed approach. To our best knowledge, our work is the first attempt to incorporate vague, imprecise information into software system survivability evaluation

LinGraph: a graph-based automated planner for concurrent task planning based on linear logic

In this paper, we introduce an automated planner for deterministic, concurrent domains, formulated as a graph-based theorem prover for a propositional fragment of intuitionistic linear logic, relying on the previously established connection between intuitionistic linear logic and planning problems. The new graph-based theorem prover we introduce improves planning performance by reducing proof permutations that are irrelevant to planning problems particularly in the presence of large numbers of objects and agents with identical properties (e.g. robots within a swarm, or parts in a large factory). We first present our graph-based automated planner, the Linear Logic Graph Planner (LinGraph). Subsequently we illustrate its application for planning within a concurrent manufacturing domain and provide comparisons with four existing automated planners, BlackBox, Symba-2, Metis and the Temporal Fast Downward (TFD), covering a wide range of state-of-the-art automated planning techniques and implementations. We show that even though LinGraph does not rely on any heuristics, it still outperforms these systems for concurrent domains with large numbers of identical objects and agents. These gains persist even when existing methods on symmetry reduction and numerical fluents are used, with LinGraph capable of handling problems with thousands of objects. Following these results, we also show that plan construction with LinGraph is equivalent to multiset rewriting systems, formally relating LinGraph to intuitionistic linear logic. © 2017, Springer Science+Business Media New York

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

Dagstuhl News January - December 2001

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Project portfolio selection problems: a review of models, uncertainty approaches, solution techniques, and case studies

Project portfolio selection has been the focus of many scholars in the last two decades. The number of studies on the strategic process has significantly increased over the past decade. Despite this increasing trend, previous studies have not been yet critically evaluated. This paper, therefore, aims to presents a comprehensive review of project portfolio selection and optimization studies focusing on the evaluation criteria, selection approach, solution approach, uncertainty modeling, and applications. This study reviews more than 140 papers on project portfolio selection research topic to identify the gaps and to present future trends. The findings show that not only the financial criteria but also social and environmental aspects of project portfolios have been focused by researchers in project portfolio selection in recent years. In addition, meta-heuristics and heuristics approach to finding the solution of mathematical models have been the critical research by scholars. Expert systems, artificial intelligence, and big data science have not been considered in project portfolio selection in the previous studies. In future, researchers can investigate the role of sustainability, resiliency, foreign investment, and exchange rates in project portfolio selection studies, and they can focus on artificial intelligence environments using big data and fuzzy stochastic optimization techniques

A Logical Framework for Systems Biology

We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological systems and temporal properties of their dynamic behaviour. To illustrate our methodology, we consider a model of the P53/Mdm2 DNA-damage repair mechanism. We prove several properties that are important for such a model to satisfy and serve to illustrate the promise of our approach. We formalize the proofs of these properties in the Coq Proof Assistant, with the help of a Lambda Prolog prover for partial automation of the proofs