Predicate Logic

Information about Predicate Logic

For the specific term, see First-order logic.

In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential and universal quantifiers. The variables could be elements in the universe, or perhaps relations or functions over the universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function".

In informal usage, the term "predicate logic" occasionally refers to first-order logic.

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First-order logic (FOL) is a formal deductive system used by mathematicians, philosophers, linguists, and computer scientists. It goes by many names, including: first-order predicate calculus (FOPC), the lower predicate calculus,
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Mathematical logic is a branch of mathematics, which grew out of symbolic logic. Subfields include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic has contributed to, and been motivated by, the study of foundations of mathematics, but
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In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.^[1] Second-order logic is in turn extended by higher-order logic and type theory.
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Many-sorted logic can reflect formally our intention, not to handle the universe as a homogenous collection of objects, but to partition them in a way that is similar to types in typeful programming.
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infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Infinitary logics have different properties from those of standard first-order logic. In particular, infinitary logics often fail to be compact or complete.
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formula is a formal syntactic object that expresses a proposition.

The exact definition of a formula depends on the particular development of formal logic in question, but a fairly typical one (specific to first-order logic) goes as follows: Formulas are defined relative to
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The term quantification has several meanings, general and specific. Primarily it covers all those acts which quantify observations and experiences by converting them into numbers through counting and measuring. It is thus the basis for mathematics and for science.
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In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. The logical operator symbol ∃ called the existential quantifier is used to denote existential quantification.
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In predicate logic, universal quantification is an attempt to formalize the notion that something (a logical predicate) is true for everything, or every relevant thing.
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The domain of discourse, sometimes called the universe of discourse, is an analytic tool used in deductive logic, especially predicate logic. It indicates the relevant set of entities that are being dealt with by quantifiers.
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Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration.
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In western philosophy, reason has had a twofold history. On the one hand, it has been taken to be objective and so to be fixed and discoverable by dialectic, analysis or study.
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The history of logic documents the development of logic as it occurs in various cultures and traditions in history. While many cultures have employed intricate systems of reasoning, logic as an explicit analysis of the methods of reasoning received sustained development originally
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Philosophical logic is the study of the more specifically philosophical aspects of logic. The term contrasts with mathematical logic, and since the development of mathematical logic in the late nineteenth century, it has come to include most of those topics traditionally
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Philosophy of logic is the branch of philosophy that is concerned with the nature and justification of systems of logic. Some fundamental questions with which it is concerned are:

Is there only one "true" logic, or are many logics equally correct?

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The metalogic of a system of logic is the formal theory of the formal logic. Results in metalogic will consist of such things as formal proofs demonstrating the soundness of the logic.
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Logic in computer science describes topics where logic is applied to computer science and artificial intelligence. These include:

Investigations into logic that are guided by applications in computer science.

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Reasoning is the mental (cognitive) process of looking for reasons for beliefs, conclusions, actions or feelings.^[1] Humans have the ability to engage in reasoning about their own reasoning using introspection.
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Deductive reasoning, according to many dictionaries^[1]^[2]^[3]^[4], is the type of reasoning that proceeds from general principles or premises to derive particular information.
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Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument are believed to support the conclusion but do not ensure it. It is used to ascribe properties or relations to types based on tokens (i.
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Abduction, or inference to the best explanation, is a method of reasoning in which one chooses the hypothesis that would, if true, best explain the relevant evidence.
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Informal logic or non-formal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial, formal, or technical language (see formal logic).
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proposition is the content of an assertion, that is, it is true-or-false and defined by the meaning of a particular piece of language. The proposition is independent of the of communication.
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Inference is the act or process of deriving a conclusion based solely on what one already knows.

Inference is studied within several different fields.

Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology.

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Only a valid argument with true premises must have a true conclusion.
The validity of an argument depends on its form, not on the truth or falsity of its premises and conclusions. Logic seeks to discover the forms of valid arguments.
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validity as it occurs in logic refers generally to a property of deductive arguments, although many logic texts apply the term to statements as well (a statement is a sentence that “has a truth value,” i.e., that is either true or false).
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Predicate Logic

Information about Predicate Logic