Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models

The VEX-93 environment as a hybrid tool for developing knowledge systems with different problem solving techniques

The paper describes VEX-93 as a hybrid environment for developing knowledge-based and problem solver systems. It integrates methods and techniques from artificial intelligence, image and signal processing and data analysis, which can be mixed. Two hierarchical levels of reasoning contains an intelligent toolbox with one upper strategic inference engine and four lower ones containing specific reasoning models: truth-functional (rule-based), probabilistic (causal networks), fuzzy (rule-based) and case-based (frames). There are image/signal processing-analysis capabilities in the form of programming languages with more than one hundred primitive functions. User-made programs are embeddable within knowledge basis, allowing the combination of perception and reasoning. The data analyzer toolbox contains a collection of numerical classification, pattern recognition and ordination methods, with neural network tools and a data base query language at inference engines's disposal. VEX-93 is an open system able to communicate with external computer programs relevant to a particular application. Metaknowledge can be used for elaborate conclusions, and man-machine interaction includes, besides windows and graphical interfaces, acceptance of voice commands and production of speech output. The system was conceived for real-world applications in general domains, but an example of a concrete medical diagnostic support system at present under completion as a cuban-spanish project is mentioned. Present version of VEX-93 is a huge system composed by about one and half millions of lines of C code and runs in microcomputers under Windows 3.1.Postprint (published version

Probabilistic Bisimulations for PCTL Model Checking of Interval MDPs

Verification of PCTL properties of MDPs with convex uncertainties has been investigated recently by Puggelli et al. However, model checking algorithms typically suffer from state space explosion. In this paper, we address probabilistic bisimulation to reduce the size of such an MDPs while preserving PCTL properties it satisfies. We discuss different interpretations of uncertainty in the models which are studied in the literature and that result in two different definitions of bisimulations. We give algorithms to compute the quotients of these bisimulations in time polynomial in the size of the model and exponential in the uncertain branching. Finally, we show by a case study that large models in practice can have small branching and that a substantial state space reduction can be achieved by our approach.Comment: In Proceedings SynCoP 2014, arXiv:1403.784

Algebraic Properties of Arbitrage: An Application to Additivity of Discount Functions

Background: This paper aims to characterize the absence of arbitrage in the context of the Arbitrage Theory proposed by Kreps (1981) and Clark (2000) which involves a certain number of well-known financial markets. More specifically, the framework of this model is a linear (topological) space X in which a (convex) cone C defines a vector ordering. There exist markets for only some of the contingent claims of X which assign a price pi to the marketed claim mi . The main purpose of this paper is to provide some novel algebraic characterizations of the no arbitrage condition and specifically to derive the decomposability of discount functions with this approach. Methods: Traditionally, this topic has been focused from a topological or probabilistic point of view. However, in this manuscript the treatment of this topic has been by using purely algebraic tools. Results: We have characterized the absence of arbitrage by only using algebraic concepts, properties and structures. Thus, we have divided these characterizations into those concerning the preference relation and those involving the cone. Conclusion: This paper has provided some novel algebraic properties of the absence of arbitrage by assuming the most general setting. The additivity of discount functions has been derived as a particular case of the general theory