Classical proofs via basic logic

1998 ◽  
pp. 203-219 ◽  
Author(s):  
Claudia Faggian
Keyword(s):  
Basic Logic

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

Probability and Random Processes

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Random Processes ◽  
Distribution Functions ◽  
Basic Logic ◽  
Heavy Tailed Distributions ◽  
Random Components ◽  
Classical Distribution ◽  
Heavy Tailed ◽  
Basic Facts ◽  
Stochastic Events ◽  
Stochastic Event

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

scholarly journals A Qualitative Theory of Cognitive Attitudes and their Change

2021 ◽  
pp. 1-31
Author(s):  
EMILIANO LORINI
Keyword(s):  
Belief Change ◽  
Qualitative Theory ◽  
The Other ◽  
Logical Framework ◽  
Basic Logic ◽  
Conditional Belief ◽  
Concepts Of Knowledge ◽  
Cognitive Attitudes ◽  
Qualitative Decision Theory ◽  
Qualitative Decision

Abstarct We present a general logical framework for reasoning about agents’ cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire, and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions.

scholarly journals Analog Low-Voltage Current-Mode Implementation of Digital Logic Gates

2003 ◽  
Vol 26 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Power Series ◽  
Low Voltage ◽  
Logic Gates ◽  
Current Mode ◽  
New Technique ◽  
Basic Logic ◽  
Spice Simulation ◽  
Simulation Results ◽  
A New Technique ◽  
Logic Functions

In this letter a new technique is introduced for implementing the basic logic functions using analog current-mode techniques. By expanding the logic functions in power series expressions, and using summers and multipliers, realization of the basic logic functions is simplified. Since no transistors are working in saturation, the problem of fan-out is alleviated. To illustrate the proposed technique, a circuit for simultaneous realization of the logic functions NOT, OR, NAND and XOR is considered. SPICE simulation results, obtained with 3 V supply, are included

Some Basic Logic Circuits of Computers

1998 ◽  
pp. 505-528
Author(s):  
Narciso Garcia ◽  
Arthur Damask ◽  
Steven Schwarz
Keyword(s):  
Logic Circuits ◽  
Basic Logic

The Use of E-learning Tools and Log Data in a Course on Basic Logic

2020 ◽  
pp. 610-620
Author(s):  
Peter Øhrstrøm ◽  
Steinar Thorvaldsen ◽  
Ulrik Sandborg-Petersen ◽  
Thomas Ploug ◽  
David Jakobsen
Keyword(s):  
Learning Tools ◽  
Basic Logic ◽  
Log Data ◽  
E Learning

The electrochemistry of corrosion Part 5: prevention and protection

1979 ◽  
Vol 26 (7) ◽  
pp. 8-11
Author(s):  
Donald Stewart
Keyword(s):  
Basic Logic

The purpose of this series is to show that there is a basic logic in the science which underlies corrosion and that this logic can lead naturally into a consideration of the methods which are available for preventing corrosion. There are many different methods and combinations of methods which can be used to prevent or reduce corrosion in metals. I have found it convenient to arrange these in separate groups, arranged according to the fundamental principles on which they are based. Practical details of the methods can be found in most textbooks on corrosion.

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