His approach also had important practical implications. Tarski’s approach revolutionized logic by making semantics mathematical. He then defined a relationship in terms of that compound structure (sentences, facts, truth) which he claimed both generated and explained the consequence relation for the language. Tarski supplemented the set of statements with a way of representing the “facts” the statements were about, and a recursive definition of truth for the statements that defined which statements were true in which sets of facts. In the original application the sentences were statements from number theory. The statements in that language were sentences in first order logic. He began with the language for which the consequence relation was to be modeled. Tarski developed a mathematical model of consequence that consisted of several parts. The original work was done by Alfred Tarski, a Polish mathematician. These properties included soundness (do the proof rules always generate valid conclusions) and completeness (does a set of axioms and proof rules generate all valid conclusions). ![]() Having a mathematical model of consequence that was independent of syntactic deductive rules enabled the properties of deductive systems to be proven. Working out a mathematically rigorous way of modeling consequence for sentences of first order logic was a fundamental advance in the field of logic. One could say it is the central concept in logic. Consequence is an aspect of semantics, the practice of modeling the meaning of expressions in languages. ![]() More formally, for some language L, for statements P and Q in L, Q is a consequence of P just in case if P is true, then Q must be true. What does that mean? Consequence is the relation that tells you, for any statement x in some language, what other statements in the language you know, if you know x. The original problem was to create an effective technique for modeling the consequence relation for object-oriented data. The published version of this work may be found here. My dissertation project developed a framework for understanding why logic works, and applied that framework to create new techniques for building models of logical consequence that are more effective for modeling the meaning of feature structures (an abstraction related to object-oriented expressions). Logicworks may also be known as or be related to Logicworks, Logicworks Corporation and Logicworks Systems Corporation.“I think what you have done in your dissertation is quite interesting and makes a real contribution to the program of understanding what we mean by logical consequence.” The data presented on this page does not represent the view of Logicworks and its employees or that of Zippia. None of the information on this page has been provided or approved by Logicworks. While we have made attempts to ensure that the information displayed are correct, Zippia is not responsible for any errors or omissions or for the results obtained from the use of this information. Sources of data may include, but are not limited to, the BLS, company filings, estimates based on those filings, H1B filings, and other public and private datasets. ![]() The data on this page is also based on data sources collected from public and open data sources on the Internet and other locations, as well as proprietary data we licensed from other companies. ![]() The employee data is based on information from people who have self-reported their past or current employments at Logicworks. Zippia gives an in-depth look into the details of Logicworks, including salaries, political affiliations, employee data, and more, in order to inform job seekers about Logicworks.
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