Teach Yourself Logic 2016: A Study Guide
... daunting length. But there is another reason which I want to highlight: I very strongly recommend tackling an area of logic by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to procee ...
... daunting length. But there is another reason which I want to highlight: I very strongly recommend tackling an area of logic by reading a series of books which overlap in level (with the next one covering some of the same ground and then pushing on from the previous one), rather than trying to procee ...
Section 1: Propositional Logic
... the basic level of structure is called propositional logic. First order predicate logic, which is often called just predicate logic, studies structure on a deeper level. • The second direction is the nature of truth. For example, one may talk about statements that are usually true or true at certain ...
... the basic level of structure is called propositional logic. First order predicate logic, which is often called just predicate logic, studies structure on a deeper level. • The second direction is the nature of truth. For example, one may talk about statements that are usually true or true at certain ...
relevant reasoning as the logical basis of
... learning engines of large-scale knowledge-based systems. To make the current knowledge-based systems more powerful and flexible, we have to solve this problem from both theoretical and practical aspects. This paper proposes that relevant reasoning based on paradox-free relevant logics should be take ...
... learning engines of large-scale knowledge-based systems. To make the current knowledge-based systems more powerful and flexible, we have to solve this problem from both theoretical and practical aspects. This paper proposes that relevant reasoning based on paradox-free relevant logics should be take ...
Proof Theory of Finite-valued Logics
... and tableaux for classical (and intuitionistic) logic. Several people have, since the 1950’s, proposed ways to generalize such formalisms from the classical to the manyvalued case. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by s ...
... and tableaux for classical (and intuitionistic) logic. Several people have, since the 1950’s, proposed ways to generalize such formalisms from the classical to the manyvalued case. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by s ...
possibilistic logic - an overview
... Possibilistic logic is a weighted logic that handles uncertainty (but it also models preferences), in a qualitative way by associating certainty, or priority levels, to classical logic formulas. Moreover, possibilistic logic copes with inconsistency by taking advantage of the stratification of the s ...
... Possibilistic logic is a weighted logic that handles uncertainty (but it also models preferences), in a qualitative way by associating certainty, or priority levels, to classical logic formulas. Moreover, possibilistic logic copes with inconsistency by taking advantage of the stratification of the s ...
Essentials Of Symbolic Logic
... discoveries was not realized at the time they were made. The general belief that all the important logical discoveries have been made by Aristotle naturally tended to prevent philosophers from assessing any new discovery at it’s true value. The undeveloped state of the mathematical sciences prior to ...
... discoveries was not realized at the time they were made. The general belief that all the important logical discoveries have been made by Aristotle naturally tended to prevent philosophers from assessing any new discovery at it’s true value. The undeveloped state of the mathematical sciences prior to ...
Completeness in modal logic - Lund University Publications
... false at w1, q alone is true at w2, and both are true at w3. Let N(w1) be {{w1, w2, w3}, {w3}}. {w1, w2, w3} is the truth-set of p ⊃ q, so (p ⊃ q) is true at w1. {w3} is the truth-set of p, so p is also true at w1. But the truth set of q is {w2, w3} and this is not in N(w1). So q fails at w1, and th ...
... false at w1, q alone is true at w2, and both are true at w3. Let N(w1) be {{w1, w2, w3}, {w3}}. {w1, w2, w3} is the truth-set of p ⊃ q, so (p ⊃ q) is true at w1. {w3} is the truth-set of p, so p is also true at w1. But the truth set of q is {w2, w3} and this is not in N(w1). So q fails at w1, and th ...
Non-Classical Logic
... tions for upper vs. lowercase for these purposes.) row represents a different possible interpretation. ...
... tions for upper vs. lowercase for these purposes.) row represents a different possible interpretation. ...
Introduction to first order logic for knowledge representation
... A language of a logic, i.e., a logical language is a formal language, which has the following characteristics: The alphabet of a logical languages typically contains basic symbols that are used to indicate the basic (atomic) components of the (part of the) world the logic is supposed to describe. Th ...
... A language of a logic, i.e., a logical language is a formal language, which has the following characteristics: The alphabet of a logical languages typically contains basic symbols that are used to indicate the basic (atomic) components of the (part of the) world the logic is supposed to describe. Th ...
From Natural Language to Soft Computing: New Paradigms
... Key Idea: ”Computation with information described in natural language (NL) is closely related to Computing with Words. NL-Computation is of intrinsic importance because much of human knowledge is described in natural language. This is particularly true in such fields as economics, data mining, syste ...
... Key Idea: ”Computation with information described in natural language (NL) is closely related to Computing with Words. NL-Computation is of intrinsic importance because much of human knowledge is described in natural language. This is particularly true in such fields as economics, data mining, syste ...
Formal deduction in propositional logic
... • Remark: In (∨−) it is the ∨ between A and B in A ∨ B that is eliminated in the conclusion C . • (¬ −) expresses the method of indirect proof or proof by contradiction: if a contradiction (denoted by B and ¬B) follows from certain premises (denoted by Σ) with an additional supposition that a certai ...
... • Remark: In (∨−) it is the ∨ between A and B in A ∨ B that is eliminated in the conclusion C . • (¬ −) expresses the method of indirect proof or proof by contradiction: if a contradiction (denoted by B and ¬B) follows from certain premises (denoted by Σ) with an additional supposition that a certai ...
FC §1.1, §1.2 - Mypage at Indiana University
... with which we began this chapter. Logical deduction will be a major topic of this chapter; under the name of proof , it will be the last major topic of this chapter, and a major tool for the rest of this book. ...
... with which we began this chapter. Logical deduction will be a major topic of this chapter; under the name of proof , it will be the last major topic of this chapter, and a major tool for the rest of this book. ...
Master Thesis - Yoichi Hirai
... Shavit [19]. The obtained model is abstract enough so that it can be described as a Kripke model of intuitionistic propositional logic equipped with additional functions on possible worlds. Two views on knowledge Original intuitionistic meaning of knowledge ...
... Shavit [19]. The obtained model is abstract enough so that it can be described as a Kripke model of intuitionistic propositional logic equipped with additional functions on possible worlds. Two views on knowledge Original intuitionistic meaning of knowledge ...
full text (.pdf)
... All the operators are monotone with respect to . In other words, if p q, then pr qr, rp rq, p + r q + r, and p q for any r. The completeness result of Kozen 1994] says that all true identities between regular expressions interpreted as regular sets of strings are derivable from the axioms of Kleene ...
... All the operators are monotone with respect to . In other words, if p q, then pr qr, rp rq, p + r q + r, and p q for any r. The completeness result of Kozen 1994] says that all true identities between regular expressions interpreted as regular sets of strings are derivable from the axioms of Kleene ...
One-dimensional Fragment of First-order Logic
... Two-variable logic and guarded-fragment are examples of decidable fragments of first-order logic that are not based on restricting the quantifier alternation patterns of formulae, unlike the prefix classes studied in the context of the classical decision problem. Surprisingly, not many such framewor ...
... Two-variable logic and guarded-fragment are examples of decidable fragments of first-order logic that are not based on restricting the quantifier alternation patterns of formulae, unlike the prefix classes studied in the context of the classical decision problem. Surprisingly, not many such framewor ...
Modal Consequence Relations
... from σ0 ; σ1 ; · · · ; σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation betwee ...
... from σ0 ; σ1 ; · · · ; σn−1 to δ is logically correct if whenever σi is true for all i < n, then so is δ. In place of ‘argument’ one also speaks of a ‘rule’ or an ‘inference’ and says that the rule is valid. This approach culminated in the notion of a consequence relation, which is a relation betwee ...
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.