Mathematical logic is something that has been around for a very long time. Centuries Ago Greek and other logicians tried to make sense out of mathematical proofs. As time went on other people tried to do the same thing but using only symbols and variables. But I will get into detail about that a little later. There is also something called set theory, which is related with this. In mathematical logic a lot of terms are used such as axiom and proofs. A lot of things in math can be proven, but there are still some things that will probably always remain theories or ideas.

Mathematical Logic is something that has a very long history behind it. It has been debated on for many centuries. If someone were to divide mathematical logic into groups they would get two major groups. Both groups are very long. One is called "The history of formal deduction" and it goes all the way back to Aristotle and Euclid and other people who lived at that time. The other is "the history of mathematical analysis" which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together.

Somebody who studies mathematical logic and gives his or her own concepts about it is called a logician. Some well known logicians include Boole and Frege. They were trying to give a definite form to what formal deduction really was. Aristotle had already done such a thing but he had done it with language, Boole wanted to do it with only Symbols. Frege came up with "Predicate Calculus".

As time went on people did not make new theories as much as they used to in the time of Aristotle. They mostly concentrated on expanding on theories that have been said centuries ago, proving those theories or putting them into symbolic form.

...Bertrand Russell's Contribution to the Development of Formal Logic
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Since the beginning of time, man has been in search of answers. These philosophical enquiries are what gave birth to everything we know, such as science, law, and religion. It has laid the foundation to which all theories and discoveries have come from, and it is the soil from which the fruits of life have grown. The formal definition of philosophy is that it 'is the study of general and fundamental problems concerning matters such as existence, knowledge, truth, justice, beauty, validity, mind and language.'[1] Based on this definition, we conclude that philosophy encompasses and addresses everything in life and beyond.
The history of philosophy dates back to approximately the sixth century B.C which proves that man has been born with the curiosity and hunger for knowledge, and that they have been in search for true meaning since the beginning of time. The timeline of philosophy is divided into three periods with a fourth period currently being established. These periods are called ancient philosophy, medieval philosophy, and early modern philosophy. The fourth and recent period is known as contemporary philosophy and it started in 1900. Many of contemporary philosophers have altered the way we view philosophy. They have introduced a new area of philosophy called analytic philosophy, and Bertrand Russell is one of the founders. In addition, he is known to be one of the two...

...1
What Is Logic?
1 Arguments
Symbolic logic is usually described as the study of the difference between valid
and invalid arguments, so we begin with an explanation of this terminology. An
argument is a piece of discourse which contains some premises, a conclusion,
and perhaps also some reasoning in which an attempt is made to derive the
conclusion from the premises. The premises are those statements which, for
the purposes of the argument, are being accepted as true. The conclusion is the
statement whose truth the argument aims to demonstrate, given acceptance of
the premises. Hence this ‘logical’ sense of ‘argument’ is quite different from its
sense in ‘Smith and Jones are having an argument’, though an argument in the
logical sense might be reconstructible from what Smith or Jones says.
For present purposes, we take an argument to consist just in a listing of the
premises, and then the conclusion. A valid argument is an argument whose
conclusion follows from its premises, and correspondingly, an invalid argument is an argument whose conclusion does not follow from its premises. Here
are two very simple arguments, one valid, the other invalid, which illustrate the
difference between the conclusion following from the premises and its not following:
A: (1) If our currency loses value then our trade deficit will narrow.
(2) Our currency will lose value.
(3) ∴ Our trade deficit will narrow.1
B: (1) If our currency loses...

...Philosophy
Essay 2: Use of LogicLogic plays a big role in our society today. In fact logic has played a big role in the advancement of civilization. There are many forms of logic and many different applications that go along with them. Logic seeks out the truth in statements through deduction and reasoning. Using logic one can test the validity of a statement just by understanding the format and the content of an argument. Logic is considered to be the science of reasoning and is mathematically inspired as it seeks an answer. Logic is not considered scientifically sound unless it is based off true premises. Sense logic is based off form it is safe to say that it is formal science.
Logic is said to have historically originated from the Ancient Greek Philosopher Aristotle. Using the teaching of universal definition from Socrates, Aristotle devised a logical system. “Aristotle holds that a proposition is a complex involving two terms, a subject and a predicate, each of which is represented grammatically with a noun. The logical form of a proposition is determined by its quantity and by it quality.”(King, Peter, and Stewart Shapiro. "THE HISTORY OF LOGIC"). Through investigation of the relationship the two terms shared Aristotle theorized that if in certain form one could determine the validity of an argument....

...Fuzzy Logic
B.Vasanth,
Electrical and Electronics Department, Rajalakshmi Engineering College
Thandalam, Chennai, India
vasanth1508@gmail.com
I. INTRODUCTION
Fuzzy logic was developed by Lotfi A. Zadeh in the 1960s in order to provide mathematical rules and functions which permitted natural language queries. Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false with resulting values ranging between 0.0 and 1.0. With fuzzy logic, it is possible to calculate the degree to which an item is a member. Fuzzy logic has rapidly become one of the most successful of today's technologies for developing sophisticated control systems. The reason for which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. It fills an important gap in engineering design methods left vacant by purely mathematical approaches (e.g. linear control design), and purely logic-based approaches (e.g. expert systems) in system design. While other approaches require accurate equations to model real-world behaviours, fuzzy design can accommodate the ambiguities of real-world human language and logic. It provides both an intuitive method for describing systems in human terms...

...References:
Agapay, Ramon B. Logic – The Essentials of Deductive Reasoning. 2nd Ed. Mandaluyung City: National Book Store, 2007.
Babor, Eddie R. LL.B. Logic- The Philosophical Discipline of Correct Thinking. Quezon City: C & E Publishing Inc. 2003.
Bachhuber, Andrew H., S.J. Introduction to Logic. New York: Appleton-Century-Crofts, Inc., 1957.
Bernardo Anunciacion Chavez, De Claro Malune G. Logic, A Modular Approach. Quezon City: Great Books Publishing. 2008.
Cruz Corazon L. Introduction to Logic, 4th Ed. Mandaluyong City: National Book Store. 1995.
Malitao, Arnel L. Essential Logic. Manila: National Book Store. 2003
Montemayor Felix. Harmony of Logic. 3rd Ed. Mandaluyong City: National Book Store. 1993
Nabor, Maria Imelda –Nery. Ph.D., Fundametals of Logic. Mandaluyong City: National Book Store, 2007.
Piñon, Manuel T. O.P. Fundamental Logic. Manila: Rex Book Store. 1973.
Sanguineti, Juan Jose. Logic. Manila: Sinag-Tala Publishers, Inc. 1982.
Trinidad, Alberto J. Being and Correct Thinking, An Introduction to Philosophy. Iloilo City: Seguiban Printers and Publishing House. 1999.
LOGICLOGIC: WHAT IT IS
The ordinary college student usually associates the word "logíc" with the ability to "reason" out. He is right. He usually is irritated with "illogical" behavior....

...
P (A or not A) = 1
P (A and not A) = 0
P (A and B) = P (A) P (B)
(when A and B are independent)
P (A and B) = P (A) P (B given A)
P (A or B) = P (A) + P(B)
(when A and B are mutually exclusive)
P (A or B) = P (A) + P (B) – P (A and B)
P (A) = 1 – P (not A)
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A Concise Introduction to Logic
NINTH EDITION
Patrick J. Hurley
University of San Diego
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...LogicLogic (from the Greek λογική, logike)[1] has two meanings: first, it describes the use of valid reasoning in some activity; second, it names the normative study of reasoning or a branch thereof.[2][3] In the latter sense, it features most prominently in the subjects of philosophy, mathematics, and computer science.
Logic was studied in several ancient civilizations, including India,[4] China,[5] Persia and Greece. In the West,logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Buddhists and Jains.
Logic is often divided into three parts; inductive reasoning, abductive reasoning, and deductive reasoning.
PHILOSOPHY OF LOGIC
Following the developments in Formal logic with symbolic logic in the late nineteenth century and mathematicallogic in the twentieth, topics traditionally treated by logic not being part of formal logic have tended to be...

...Know About Logic Models But Were Afraid to Ask
This paper addresses situations where a private foundation designs an initiative and awards grants to a number of sites to participate in the initiative in their local setting. The basic ideas are applicable to other situations.
What is a Logic Model?
The term "logic model" comes from the evaluation field, but these models don’t just belong to evaluators or the evaluation plan. As the term suggests, they are a basic element of programming that communicates the logic behind a program, its rationale. A logic model’s purpose is to communicate the underlying "theory" or set of assumptions or hypotheses that program proponents have about why the program will work, or about why it is a good solution to an identified problem.
Logic models are typically diagrams, flow sheets, or some other type of visual schematic that conveys relationships between contextual factors and programmatic inputs, processes, and outcomes. Logic models can come in all shapes and sizes: boxes with connecting lines that are read from left to right (or top to bottom); circular loops with arrows going in or out; or other visual metaphors and devices. What these schemata have in common are they attempt to show the links in a chain of reasoning about "what causes what," in relationship to the desired outcome or goal. The desired outcome or goal is usually...