We introduce new types of probability operators of the form QF, where F is a recursive rational subset of 0,1. A formula QFα is satisfied in a probability model if the measure of the set of worlds ...that satisfy α is in F. The new operators are suitable for describing events in discrete sample spaces. We provide sound and complete axiomatic systems for a number of probability logics augmented with the QF-operators. We show that the new operators are not definable in languages of probability logics that have been used so far. We study decidability of the presented logics. We describe a relation of 'being more expressive' between the new probability logics. Key words: Probability logic, completeness, decidability.
A propositional logic is defined which in addition to propositional language contains a list of probabilistic operators of the form P greater than or equal to s (with the intended meaning "the ...probability is at least s"). The axioms and rules syntactically determine that ranges of probabilities in the corresponding models are always finite. The completeness theorem is proved. It is shown that completeness cannot be generalized to arbitrary theories. PUBLICATION ABSTRACT
The paper presents a sound and strongly complete axiomatization of reasoning about polynomial weight formulas. In addition, the PSPACE decision procedure for polynomial weight formulas developed by ...Fagin, Halpern and Megiddo works for our logic as well. The introduced formalism allows the expression of qualitative probability statements, conditional probability and Bayesian inference.
We present a prepositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripke-like probabilistic models is defined to give ...semantics to probabilistic formulas. Every possible world of such a model is equipped with a probability space. The corresponding probabilities may have nonstandard values. The proposition "the probability is close to r" means that there is an infinitesimal ?, such that the probability is equal to r ? ? (or r + ?). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.
Qualitative Possibilities and Necessities Perović, Aleksandar; Ognjanović, Zoran; Rašković, Miodrag ...
Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Book Chapter
Recenzirano
Qualitative possibilities and necessities are well known types of confidence relations. They have been extensively studied semantically, as relations on Boolean algebras (or equivalently, relations ...on algebras of sets). The aim of this paper is to give a syntactical flavor to the subject providing a sound and complete axiomatization of qualitative possibility relations.
Interpolative Boolean Logic Radojević, Dragan; Perović, Aleksandar; Ognjanović, Zoran ...
Artificial Intelligence: Methodology, Systems, and Applications
Book Chapter
Recenzirano
A polyvalent propositional logic \documentclass12pt{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
...\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$\mathcal L$\end{document} is in Boolean frame if the set of all \documentclass12pt{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$\mathcal L$\end{document}-valid formulas coincides with the set of all tautologies. It is well known that the polyvalent logics based on the truth functionality principle are not in the Boolean frame. Interpolative Boolean logic (IBL) is a real-valued propositional logic that is in Boolean frame. The term “interpolative” cames from the fact that semantics of IBL is based on the notion of a generalized Boolean polynomial, where multiplication can be substituted by any continuous t-norm \documentclass12pt{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$*:0,1^2\longrightarrow 0,1$\end{document} such that \documentclass12pt{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$xy\leqslant x* y$\end{document}. Possible applications are illustrated with several examples.
The objective of this study was to investigate the modification of materials used in wastewater treatment for possible antimicrobial application(s). Granulated activated carbon (GAC) and natural ...clinoptilolite (CLI) were activated using Cu
- and Zn
- ions and the disinfection ability of the resulting materials was tested. Studies of the sorption and desorption kinetics were performed in order to determine and clarify the antimicrobial activity of the metal-activated sorbents. The exact sorption capacities of the selected sorbents, GAC and CLI, activated through use of Cu
- ions, were 15.90 and 3.60mg/g, respectively, while for the materials activated by Zn
- ions, the corresponding capacities were 14.00 and 4.72mg/g,. The desorption rates were 2 and 3 orders of magnitude lower than their sorption efficacy for the Cu
-, and Zn
-activated sorbents, respectively. The intermediate sorption capacity and low desorption rate indicated that the overall antimicrobial activity of the metal-modified sorbents was a result of metal ions immobilized onto surface sites. The effect of antimicrobial activity of free ions desorbed from the metal-activated surface may thus be disregarded. The antimicrobial activities of Cu/GAC, Zn/GAC, Cu/CLI and Zn/CLI were also tested against Escherichia coli, Staphylococcus aureus, and Candida albicans. After 15min exposure, the highest levels of cell inactivation were obtained through the Cu/CLI and the Cu/GAC against E. coli, 100.0 and 98.24%, respectively. However, for S. aureus and yeast cell inactivation, all Cu
- and Zn
-activated sorbents proved to be unsatisfactory. A characterization of the sorbents was performed by X-ray diffraction (XRD), X-ray photo electron spectroscopy (XPS), and field emission scanning electron microscopy (FE-SEM). A concentration of the adsorbed and released ions was determined by inductively coupled plasma-optical emission spectroscopy (ICP-OES) and mass spectrometry (ICP-MS). The results showed that the antimicrobial performance of the activated sorbents depended on the surface characteristics of the material, which itself designates the distribution and the bioavailability of the activating agent.
PDF