Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

Probabilistic Dynamic Logic of Phenomena and Cognition

The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or fuzziness of similarity measures to the uncertainty of models. These logics are based on the following fundamental notions: generality relation, uncertainty relation, simplicity relation, similarity maximization problem with empirical content and enhancement (learning) operator. We develop these notions in terms of logic and probability and developed a Probabilistic Dynamic Logic of Phenomena and Cognition (P-DL-PC) that relates to the scope of probabilistic models of brain. In our research the effectiveness of suggested formalization is demonstrated by approximation of the expert model of breast cancer diagnostic decisions. The P-DL-PC logic was previously successfully applied to solving many practical tasks and also for modelling of some cognitive processes.Comment: 6 pages, WCCI 2010 IEEE World Congress on Computational Intelligence July, 18-23, 2010 - CCIB, Barcelona, Spain, IJCNN, IEEE Catalog Number: CFP1OUS-DVD, ISBN: 978-1-4244-6917-8, pp. 3361-336

The Monotonicity And Sub-Additivity Properties Of Fuzzy Inference Systems And Their Applications

The Fuzzy Inference System (FIS) is a popular computing paradigm for undertaking modelling, control, and decision-making problems. In this thesis, the focus of investigation is on two theoretical properties of an FIS model, i.e., the monotonicity and sub-additivity properties. These properties are defined, and their applicability to tackling real-world problems is discussed. This research contributes to formulating a systematic procedure that is based on a mathematical foundation (i.e., the sufficient conditions) to develop monotonicity-preserving FIS models. A method to improve the sub-additivity property is also proposed

An Evolutionary-Based Similarity Reasoning Scheme for Monotonic Multi-Input Fuzzy Inference Systems

In this paper, an Evolutionary-based Similarity Reasoning (ESR) scheme for preserving the monotonicity property of the multi-input Fuzzy Inference System (FIS) is proposed. Similarity reasoning (SR) is a useful solution for undertaking the incomplete rule base problem in FIS modeling. However, SR may not be a direct solution to designing monotonic multi-input FIS models, owing to the difficulty in getting a set of monotonically-ordered conclusions. The proposed ESR scheme, which is a synthesis of evolutionary computing, sufficient conditions, and SR, provides a useful solution to modeling and preserving the monotonicity property of multi-input FIS models. A case study on Failure Mode and Effect Analysis (FMEA) is used to demonstrate the effectiveness of the proposed ESR scheme in undertaking real world problems that require the monotonicity property of FIS models

The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this chapter, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of this new approach. The last part of this chapter concerns the presentation of the neutrosophic logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and neutrosophic logic are useful tools in decision making after fusioning the information using the DSm hybrid rule of combination of masses.Comment: 20 page