Showing posts with label Symbolic Logic. Show all posts
Showing posts with label Symbolic Logic. Show all posts

AI - Symbolic Logic


In mathematical and philosophical reasoning, symbolic logic entails the use of symbols to express concepts, relations, and positions.

Symbolic logic varies from (Aristotelian) syllogistic logic in that it employs ideographs or a particular notation to "symbolize exactly the item discussed" (Newman 1956, 1852), and it may be modified according to precise rules.

Traditional logic investigated the truth and falsehood of assertions, as well as their relationships, using terminology derived from natural language.

Unlike nouns and verbs, symbols do not need interpretation.

Because symbol operations are mechanical, they may be delegated to computers.

Symbolic logic eliminates any ambiguity in logical analysis by codifying it entirely inside a defined notational framework.

Gottfried Wilhelm Leibniz (1646–1716) is widely regarded as the founding father of symbolic logic.

Leibniz proposed the use of ideographic symbols instead of natural language in the seventeenth century as part of his goal to revolutionize scientific thinking.

Leibniz hoped that by combining such concise universal symbols (characteristica universalis) with a set of scientific reasoning rules, he could create an alphabet of human thought that would promote the growth and dissemination of scientific knowledge, as well as a corpus containing all human knowledge.

Boolean logic, the logical underpinnings of mathematics, and decision issues are all topics of symbolic logic that may be broken down into subcategories.

George Boole, Alfred North Whitehead, and Bertrand Russell, as well as Kurt Gödel, wrote important contributions in each of these fields.

George Boole published The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought in the mid-nineteenth century (1854).

Boole zoomed down on a calculus of deductive reasoning, which led him to three essential operations in a logical mathematical language known as Boolean algebra: AND, OR, and NOT.

The use of symbols and operators greatly aided the creation of logical formulations.

Claude Shannon (1916–2001) employed electromechanical relay circuits and switches to reproduce Boolean algebra in the twentieth century, laying crucial foundations in the development of electronic digital computing and computer science in general.

Alfred North Whitehead and Bertrand Russell established their seminal work in the subject of symbolic logic in the early twentieth century.

Their Principia Mathematica (1910, 1912, 1913) demonstrated how all of mathematics may be reduced to symbolic logic.

Whitehead and Russell developed a logical system from a handful of logical concepts and a set of postulates derived from those ideas in the first book of their work.

Whitehead and Russell established all mathematical concepts, including number, zero, successor of, addition, and multiplication, using fundamental logical terminology and operational principles like proposition, negation, and either-or in the second book of the Principia.

In the last and third volumes, Whitehead and Russell were able to demonstrate that the nature and reality of all mathematics is built on logical concepts and connections.

The Principia showed how every mathematical postulate might be inferred from previously explained symbolic logical facts.

Only a few decades later, Kurt Gödel's On Formally Undecidable Propositions in the Principia Mathematica and Related Systems (1931) critically analyzed the Principia's strong and deep claims, demonstrating that Whitehead and Russell's axiomatic system could not be consistent and complete at the same time.

Even so, it required another important book in symbolic logic, Ernst Nagel and James Newman's Gödel's Proof (1958), to spread Gödel's message to a larger audience, including some artificial intelligence practitioners.

Each of these seminal works in symbolic logic had a different influence on the development of computing and programming, as well as our understanding of a computer's capabilities as a result.

Boolean logic has made its way into the design of logic circuits.

The Logic Theorist program by Simon and Newell provided logical arguments that matched those found in the Principia Mathematica, and was therefore seen as evidence that a computer could be programmed to do intelligent tasks via symbol manipulation.

Gödel's incompleteness theorem raises intriguing issues regarding how programmed machine intelligence, particularly strong AI, will be realized in the end.

~ Jai Krishna Ponnappan

Find Jai on Twitter | LinkedIn | Instagram

You may also want to read more about Artificial Intelligence here.

See also: 

Symbol Manipulation.

References And Further Reading

Boole, George. 1854. Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities. London: Walton.

Lewis, Clarence Irving. 1932. Symbolic Logic. New York: The Century Co.

Nagel, Ernst, and James R. Newman. 1958. Gödel’s Proof. New York: New York University Press.

Newman, James R., ed. 1956. The World of Mathematics, vol. 3. New York: Simon and Schuster.

Whitehead, Alfred N., and Bertrand Russell. 1910–1913. Principia Mathematica. Cambridge, UK: Cambridge University Press.

Artificial Intelligence - Who Was John McCarthy?


John McCarthy  (1927–2011) was an American computer scientist and mathematician who was best known for helping to develop the subject of artificial intelligence in the late 1950s and pushing the use of formal logic in AI research.

McCarthy was a creative thinker who earned multiple accolades for his contributions to programming languages and operating systems research.

Throughout McCarthy's life, however, artificial intelligence and "formalizing common sense" remained his primary research interest (McCarthy 1990).

As a graduate student, McCarthy first met the concepts that would lead him to AI at the Hixon conference on "Cerebral Mechanisms in Behavior" in 1948.

The symposium was place at the California Institute of Technology, where McCarthy had just finished his undergraduate studies and was now enrolled in a graduate mathematics program.

In the United States, machine intelligence had become a subject of substantial academic interest under the wide term of cybernetics by 1948, and many renowned cyberneticists, notably Princeton mathematician John von Neumann, were in attendance at the symposium.

McCarthy moved to Princeton's mathematics department a year later, when he discussed some early ideas inspired by the symposium with von Neumann.

McCarthy never published the work, despite von Neumann's urging, since he believed cybernetics could not solve his problems concerning human knowing.

McCarthy finished a PhD on partial differential equations at Princeton.

He stayed at Princeton as an instructor after graduating in 1951, and in the summer of 1952, he had the chance to work at Bell Labs with cyberneticist and inventor of information theory Claude Shannon, whom he persuaded to collaborate on an edited collection of writings on machine intelligence.

Automata Studies received contributions from a variety of fields, ranging from pure mathematics to neuroscience.

McCarthy, on the other hand, felt that the published studies did not devote enough attention to the important subject of how to develop intelligent machines.

McCarthy joined the mathematics department at Stanford in 1953, but was fired two years later, maybe because he spent too much time thinking about intelligent computers and not enough time working on his mathematical studies, he speculated.

In 1955, he accepted a position at Dartmouth, just as IBM was preparing to establish the New England Computation Center at MIT.

The New England Computation Center gave Dartmouth access to an IBM computer that was installed at MIT and made accessible to a group of New England colleges.

McCarthy met IBM researcher Nathaniel Rochester via the IBM initiative, and he recruited McCarthy to IBM in the summer of 1955 to work with his research group.

McCarthy persuaded Rochester of the need for more research on machine intelligence, and he submitted a proposal to the Rockefeller Foundation for a "Summer Research Project on Artificial Intelligence" with Rochester, Shannon, and Marvin Minsky, a graduate student at Princeton, which included the first known use of the phrase "artificial intelligence." Despite the fact that the Dartmouth Project is usually regarded as a watershed moment in the development of AI, the conference did not go as McCarthy had envisioned.

The Rockefeller Foundation supported the proposal at half the proposed budget since it was for such an unique field of research with a relatively young professor as author, and because Shannon's reputation carried substantial weight with the Foundation.

Furthermore, since the event took place over many weeks in the summer of 1955, only a handful of the guests were able to attend the whole period.

As a consequence, the Dartmouth conference was a fluid affair with an ever-changing and unpredictably diverse guest list.

Despite its chaotic implementation, the meeting was crucial in establishing AI as a distinct area of research.

McCarthy won a Sloan grant to spend a year at MIT, closer to IBM's New England Computation Center, while still at Dartmouth in 1957.

McCarthy was given a post in the Electrical Engineering department at MIT in 1958, which he accepted.

Later, he was joined by Minsky, who worked in the mathematics department.

McCarthy and Minsky suggested the construction of an official AI laboratory to Jerome Wiesner, head of MIT's Research Laboratory of Electronics, in 1958.

McCarthy and Minsky agreed on the condition that Wiesner let six freshly accepted graduate students into the laboratory, and the "artificial intelligence project" started teaching its first generation of students.

McCarthy released his first article on artificial intelligence in the same year.

In his book "Programs with Common Sense," he described a computer system he named the Advice Taker that would be capable of accepting and understanding instructions in ordinary natural language from nonexpert users.

McCarthy would later define Advice Taker as the start of a study program aimed at "formalizing common sense." McCarthy felt that everyday common sense notions, such as comprehending that if you don't know a phone number, you'll need to look it up before calling, might be written as mathematical equations and fed into a computer, enabling the machine to come to the same conclusions as humans.

Such formalization of common knowledge, McCarthy felt, was the key to artificial intelligence.

McCarthy's presentation, which was presented at the United Kingdom's National Physical Laboratory's "Symposium on Mechansation of Thought Processes," helped establish the symbolic program of AI research.

McCarthy's research was focused on AI by the late 1950s, although he was also involved in a range of other computing-related topics.

In 1957, he was assigned to a group of the Association for Computing Machinery charged with developing the ALGOL programming language, which would go on to become the de facto language for academic research for the next several decades.

He created the LISP programming language for AI research in 1958, and its successors are widely used in business and academia today.

McCarthy contributed to computer operating system research via the construction of time sharing systems, in addition to his work on programming languages.

Early computers were large and costly, and they could only be operated by one person at a time.

McCarthy identified the necessity for several users throughout a major institution, such as a university or hospital, to be able to use the organization's computer systems concurrently via computer terminals in their offices from his first interaction with computers in 1955 at IBM.

McCarthy pushed for study on similar systems at MIT, serving on a university committee that looked into the issue and ultimately assisting in the development of MIT's Compatible Time-Sharing System (CTSS).

Although McCarthy left MIT before the CTSS work was completed, his advocacy with J.C.R.

Licklider, future office head at the Advanced Research Projects Agency, the predecessor to DARPA, while a consultant at Bolt Beranek and Newman in Cambridge, was instrumental in helping MIT secure significant federal support for computing research.

McCarthy was recruited to join what would become the second department of computer science in the United States, after Purdue's, by Stanford Professor George Forsythe in 1962.

McCarthy insisted on going only as a full professor, which he believed would be too much for Forsythe to handle as a young researcher.

Forsythe was able to persuade Stanford to grant McCarthy a full chair, and he moved to Stanford in 1965 to establish the Stanford AI laboratory.

Until his retirement in 2000, McCarthy oversaw research at Stanford on AI topics such as robotics, expert systems, and chess.

McCarthy was up in a family where both parents were ardent members of the Communist Party, and he had a lifetime interest in Russian events.

He maintained numerous professional relationships with Soviet cybernetics and AI experts, traveling and lecturing there in the mid-1960s, and even arranged a chess match between a Stanford chess computer and a Russian equivalent in 1965, which the Russian program won.

He developed many foundational concepts in symbolic AI theory while at Stanford, such as circumscription, which expresses the idea that a computer must be allowed to make reasonable assumptions about problems presented to it; otherwise, even simple scenarios would have to be specified in such exacting logical detail that the task would be all but impossible.

McCarthy's accomplishments have been acknowledged with various prizes, including the 1971 Turing Award, the 1988 Kyoto Prize, admission into the National Academy of Sciences in 1989, the 1990 Presidential Medal of Science, and the 2003 Benjamin Franklin Medal.

McCarthy was a brilliant thinker who continuously imagined new technologies, such as a space elevator for economically transporting stuff into orbit and a system of carts strung from wires to better urban transportation.

In a 2008 interview, McCarthy was asked what he felt the most significant topics in computing now were, and he answered without hesitation, "Formalizing common sense," the same endeavor that had inspired him from the start.

~ Jai Krishna Ponnappan

Find Jai on Twitter | LinkedIn | Instagram

You may also want to read more about Artificial Intelligence here.

See also: 

Cybernetics and AI; Expert Systems; Symbolic Logic.

References & Further Reading:

Hayes, Patrick J., and Leora Morgenstern. 2007. “On John McCarthy’s 80th Birthday, in Honor of His Contributions.” AI Magazine 28, no. 4 (Winter): 93–102.

McCarthy, John. 1990. Formalizing Common Sense: Papers, edited by Vladimir Lifschitz. Norwood, NJ: Albex.

Morgenstern, Leora, and Sheila A. McIlraith. 2011. “John McCarthy’s Legacy.” Artificial Intelligence 175, no. 1 (January): 1–24.

Nilsson, Nils J. 2012. “John McCarthy: A Biographical Memoir.” Biographical Memoirs of the National Academy of Sciences.

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