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Introduction
Published in Ali Zilouchian, Mo Jamshidi, Intelligent Control Systems Using Soft Computing Methodologies, 2001
The Modus Ponens deduction is used as a tool for inferencing in rule-based systems. A typical IF-THEN rule is used to determine whether an antecedent (cause or action) infers a consequent (effect or action). Suppose we have a rule of the form, IFA,THENB
Fuzzy Systems—Sets, Logic, and Control
Published in Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi, Intelligent Control Systems with an Introduction to System of Systems Engineering, 2018
Thrishantha Nanayakkara, Ferat Sahin, Mo Jamshidi
The modus ponens deduction is used as a tool for inferencing in rule-based systems. A typical IF-THEN rule is used to determine whether an antecedent (cause or action) infers a consequent (effect or action). Suppose we have a rule of the form IFA,THENB
M
Published in Philip A. Laplante, Comprehensive Dictionary of Electrical Engineering, 2018
modus tollens a specific trinary logic truth table for this number system. modified z-transform a z-transform of signals and systems that contain nonzero deadtime in the range 0 <T where T is the sampling interval. Modified ztransforms are usually derived from fundamental principles and given as separate columns in z-transform tables for standard functions. modified-return-to-bias recording netic recording code. See magmodulating signal the baseband source signal used to encode information onto a carrier wave by varying one or more of its characteristics (e.g., the amplitude, frequency, or phase of a sinusoid; or the amplitude, width, repetition rate, or position of each pulse in a periodic pulse train). modulation (1) variation of the amplitude or phase of an electromagnetic wave. (2) the process of encoding an informationcarrying waveform onto a carrier waveform, typically in preparation for transmission. See amplitude modulation, frequency modulation, phase modulation. modulation efficiency ratio of the baseband bit rate to the transmission bandwidth after modulation. modulation index for an angle-modulated signal, the modulation index is the ratio of the maximum modulation deviation to the modulating frequency, and represents the maximum phase deviation in the modulating signal. modulation property a property of the Fourier transform in which the Fourier transform of a modulated signal c(t)e jw o t is equal to C(w - w o ), where C(w) is the Fourier transform of c(t). modulation transfer function (MTF) for an imaging system the Fourier transform of the system line spread function. The MTF describes the spatial frequency resolution of the system. modulator device that varies the amplitude or phase of an electromagnetic wave. modus ponens a rule of reasoning which states that given that two propositions, A and A B (implication), are true, then it can be inferred that B is also true. modus tollens a rule of reasoning which states that if a proposition B is not true and given that
Vagueness as an epiphenomenon, and non-transitivity
Published in Journal of Applied Non-Classical Logics, 2022
In addition, the rule of modus ponens turns out to be logically valid. Indeed, let us consider two sentences B, C, and suppose that there is an interpretation M of the language such that it is not the case that . This means that . Since it is and , it follows that , and since we have that , we conclude that . But we also have that . We conclude that the modus ponens rule is valid in relation to any interpretation of the language, a fact we abbreviate as .