On continuity of the entropy-based differently implicational algorithm

summary:Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism

Attribute Exploration of Gene Regulatory Processes

This thesis aims at the logical analysis of discrete processes, in particular of such generated by gene regulatory networks. States, transitions and operators from temporal logics are expressed in the language of Formal Concept Analysis. By the attribute exploration algorithm, an expert or a computer program is enabled to validate a minimal and complete set of implications, e.g. by comparison of predictions derived from literature with observed data. Here, these rules represent temporal dependencies within gene regulatory networks including coexpression of genes, reachability of states, invariants or possible causal relationships. This new approach is embedded into the theory of universal coalgebras, particularly automata, Kripke structures and Labelled Transition Systems. A comparison with the temporal expressivity of Description Logics is made. The main theoretical results concern the integration of background knowledge into the successive exploration of the defined data structures (formal contexts). Applying the method a Boolean network from literature modelling sporulation of Bacillus subtilis is examined. Finally, we developed an asynchronous Boolean network for extracellular matrix formation and destruction in the context of rheumatoid arthritis.Comment: 111 pages, 9 figures, file size 2.1 MB, PhD thesis University of Jena, Germany, Faculty of Mathematics and Computer Science, 2011. Online available at http://www.db-thueringen.de/servlets/DocumentServlet?id=1960

Towards a corpus-based analysis of evaluative scales associated with even

Scalar focus operators like even, only, etc. interact with scales, i. e., ordered sets of alternatives that are referenced by focus structure. The scaling dimensions interacting with focus operators have been argued to be semantic (e. g. entailment relations, probability) in earlier work, but it has been shown that purely semantic analyses are too restrictive, and that the specific scale that a given operator interacts with is often pragmatic, in the sense of being a function of the context. If that is true, the question arises what exactly determines the (types of) scales interacting with focus operators. The present study addresses this question by investigating the distributional behaviour of the additive scalar particle even relative to scales whose focus alternatives are ordered in terms of evaluative attitudes (positive, negative). Our hypothesis is that such evaluative attitudinal scales are at least partially functions of the lexical material in the sentential environment. This hypothesis is tested by determining correlations between sentence-level attitudes and lexically encoded attitudes in the relevant sentences. We use data from the Europarl corpus, a corpus of scripted and highly elaborated political speech, which is rich in argumentative discourse and thus lends itself to the study of attitudes in context. Our results show that there are in fact significant correlations between (manual) sentence-level evaluations and lexical evaluations (determined through machine learning) in the textual environment of the relevant operators. We conclude with an outlook on possible extensions of the method applied in the present study by identifying attitudinal patterns beyond the sentence, showing that positively and negatively connotated instances of even differ in terms of their argumentative function, with positive even often marking the climax and endpoint of an argument, while negative even often occurs in qualifying insertions like concessive parentheses. While we regard our results as valid, some refinements and extensions of the method are pointed out as necessary steps towards the establishment of an empirical sentence semantics, in the domain of scalar additive operators as well as more generally speaking

The foundation of capability modelling: A study of the impact and utilisation of human resources

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research aims at finding a foundation for assessment of capabilities and applying the concept in a human resource selection. The research identifies a common ground for assessing individuals’ applied capability in a given job based on literature review of various disciplines in engineering, human sciences and economics. A set of criteria is found to be common and appropriate to be used as the basis of this assessment. Applied Capability is then described in this research as the impact of the person in fulfilling job requirements and also their level of usage from their resources with regards to the identified criteria. In other words how their available resources (abilities, skills, value sets, personal attributes and previous performance records) can be used in completing a job. Translation of the person’s resources and task requirements using the proposed criteria is done through a novel algorithm and two prevalent statistical inference techniques (OLS regression and Fuzzy) are used to estimate quantitative levels of impact and utilisation. A survey on post graduate students is conducted to estimate their applied capabilities in a given job. Moreover, expert academics are surveyed on their views on key applied capability assessment criteria, and how different levels of match between job requirement and person’s resources in those criteria might affect the impact levels. The results from both surveys were mathematically modelled and the predictive ability of the conceptual and mathematical developments were compared and further contrasted with the observed data. The models were tested for robustness using experimental data and the results for both estimation methods in both surveys are close to one another with the regression models being closer to observations. It is believed that this research has provided sound conceptual and mathematical platforms which can satisfactorily predict individuals’ applied capability in a given job. This research has contributed to the current knowledge and practice by a) providing a comparison of capability definitions and uses in different disciplines, b) defining criteria for applied capability assessment, c) developing an algorithm to capture applied capabilities, d) quantification of an existing parallel model and finally e) estimating impact and utilisation indices using mathematical methods

Metaphor as a device for understanding cognitive concepts

The paper addresses metaphor as a cognitive-semantic device which is able to reveal intuitive mechanisms of the thinking process, thus filling the gaps in the sphere of logically objective human knowledge and opening the possibility to describe abstract concepts of the human mind in terms. This paper substantiates the principal possibility of conceptual modeling of the metaphorization process and describes its baseline algorithm, identifies complex metaphors and establishes the cognitive-semantic features of their functioning. The main conclusion of the reasoning confirms the hypothesis that different image schemes have different strength of heuristic potential, which determines the fullness of metaphorical descriptions of concepts

Zero-one laws with respect to models of provability logic and two Grzegorczyk logics

It has been shown in the late 1960s that each formula of first-order logic without constants and function symbols obeys a zero-one law: As the number of elements of finite models increases, every formula holds either in almost all or in almost no models of that size. Therefore, many properties of models, such as having an even number of elements, cannot be expressed in the language of first-order logic. Halpern and Kapron proved zero-one laws for classes of models corresponding to the modal logics K, T, S4, and S5 and for frames corresponding to S4 and S5. In this paper, we prove zero-one laws for provability logic and its two siblings Grzegorczyk logic and weak Grzegorczyk logic, with respect to model validity. Moreover, we axiomatize validity in almost all relevant finite models, leading to three different axiom systems

An evaluation methodology for the level of service at the airport landside system

A methodology is proposed for evaluating the level of service within an airport landside system from the passenger's point of view using linguistic service criteria. The new concept of level of service for a transport system, particularly within the airports indicates that there must be strong stimulation in order to proceed with the current stereotyped service standards which are being criticised due to their being based on, either physical capacity/volume or temporal/spatial standards that directly incorporates the perception of passengers, the dominant users. Most service evaluation methodologies have been concentrated on the factors of the time spent and the space provided. These quantitative factors are reasonably simple to measure but represent a narrow approach. Qualitative service level attributes are definitely important factors when evaluating the level of service from a user's point of view. This study has adopted three main evaluation factors: temporal or spatial factors as quantitative measurements and comfort factors and reasonable service factors as qualitative measurements. The service level evaluation involves the passenger's subjective judgement as a perception for service provision. To evaluate the level of service in the airport landside system from the user's perception, this research proposes to apply a multi-decision model using fuzzy set theory, in particular fuzzy approximate reasoning. Fuzzy set theory provides a strict mathematical framework for vague conceptual phenomena and a modelling language for real situations. The multi-decision model was applied to a case study at Kimpo International Airport in Seoul, Korea. Results are presented in terms of passenger satisfaction and dissatisfaction with a variety of different values

Synonymy and Identity of Proofs - A Philosophical Essay

The main objective of the dissertation is to investigate from a strictly philosophical perspective different approaches and results related to the problem of identity of proofs, which is a problem of general proof theory at the intersection of mathematics and philosophy. The author characterizes,compares and evaluates a range of formal criteria of proof-identity that have been proposed in the proof-theoretic literature. While these proposals come from mathematical logicians, the author’s background in both mathematical logic and philosophy allows him to present and discuss these proposals in a manner that is accessible to and fruitful for philosophers, especially those working in logic and philosophy of mathematics, as well as mathematical logicians. The dissertation is structured into a prologue and five sections. In the prologue, the author traces the development of the concept of a proof in ancient philosophy, culminating in the work of Aristotle. In Section I, the author turns to the roots of proof theory in modern philosophy, offering a detailed interpretation of Kant’s “Die falsche Spitzfindigkeit der vier syllogistischen Figuren”, which uncovers interesting links between Kant’s inferences of understanding and of reason and modern proof-theoretic semantics. In Section II, the author turns from historical to systematic considerations concerning different kinds of identity-criteria of proofs, ranging from overly liberal criteria that trivialize proof identity to overly strict, syntactical criteria. In Section III, the heart of the dissertation, the author offers a thorough philosophical discussion of the normalisation thesis. In Section IV, the author considers the difficulties encountered in his discussion of identity of proofs --- particularly of the normalisation thesis --- through the lens of a discussion of the notion of synonymy, and compares this thesis with other possible formal accounts of identity of proofs. In particular, by recourse to Carnap’s notion of synonymy, developed in “Meaning and Necessity”, the author proposes a notion of synonymy of proofs. In Section V, the final substantial section, the author compares the normalisation thesis to the Church-Turing thesis, thereby adducing another dimension of evaluation of the former