Relevant and Substructural Logics
... ponens is written in the form using a turnstile to echo the general definition of logical consequence in a Hilbert system. Given a set X of formulas, and a single formula A, we say that A can be proved from X (which I write “X ⇒ A”) if and only if there is a proof in the Hilbert system with A as the ...
... ponens is written in the form using a turnstile to echo the general definition of logical consequence in a Hilbert system. Given a set X of formulas, and a single formula A, we say that A can be proved from X (which I write “X ⇒ A”) if and only if there is a proof in the Hilbert system with A as the ...
Modal Languages and Bounded Fragments of Predicate Logic
... characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover ...
... characterized by its use of only bounded quantification. This so-called guarded fragment enjoys the above nice properties, including decidability, through an effectively bounded finite model property. (These are new results, obtained by generalizing notions and techniques from modal logic.) Moreover ...
Default Logic (Reiter) - Department of Computing
... where γ, α1 , . . . , αm , βm+1 , . . . , βn can be any formulas. The above would be written as a default rule like this: α1 ∧ · · · ∧ αm : ¬βm+1 , . . . , ¬βn γ Informally: ¬βi is consistent when βi is not derivable, and βi is not derivable corresponds to negation by failure not βi ...
... where γ, α1 , . . . , αm , βm+1 , . . . , βn can be any formulas. The above would be written as a default rule like this: α1 ∧ · · · ∧ αm : ¬βm+1 , . . . , ¬βn γ Informally: ¬βi is consistent when βi is not derivable, and βi is not derivable corresponds to negation by failure not βi ...
A Classification and Survey of Preference Handling Approaches in
... We have the following set of not-necessarily independent criteria for classifying approaches to preference: Host system Previously (during the 1990’s) default logic [Reiter,1980] was by-and-large the host system of choice, in that the majority of approaches to adding preferences added them to defau ...
... We have the following set of not-necessarily independent criteria for classifying approaches to preference: Host system Previously (during the 1990’s) default logic [Reiter,1980] was by-and-large the host system of choice, in that the majority of approaches to adding preferences added them to defau ...
Inferring preferred extensions by Pstable semantics
... The problem of characterizing abstract argumentation semantics does not only depend of the codification but also in the logic programming semantics. In fact, to find a suitable logic programming semantic is as important as to find a suitable codification for characterizing a particular abstract arg ...
... The problem of characterizing abstract argumentation semantics does not only depend of the codification but also in the logic programming semantics. In fact, to find a suitable logic programming semantic is as important as to find a suitable codification for characterizing a particular abstract arg ...
Logic and Artificial Intelligence - EECS @ Michigan
... 1. Contributions to branches of logical theory directly related to philosophical concerns, such as inductive logic, modal logic, deontic logic, quantum logic, tense logic, free logic, logic of questions, logic of commands, logic of preference, logic of conditionals, many-valued logic, relevance logi ...
... 1. Contributions to branches of logical theory directly related to philosophical concerns, such as inductive logic, modal logic, deontic logic, quantum logic, tense logic, free logic, logic of questions, logic of commands, logic of preference, logic of conditionals, many-valued logic, relevance logi ...
Relevant deduction
... distinction is not very deep. I don’t think there exists a sharp or deep distinction between ‘strict’ and ‘loose’ paradoxes. It rather seems to me a matter of the degree of evidence of those intuitions which turn out to be inconsistent after formalization. The paradoxes mentioned have been disappoin ...
... distinction is not very deep. I don’t think there exists a sharp or deep distinction between ‘strict’ and ‘loose’ paradoxes. It rather seems to me a matter of the degree of evidence of those intuitions which turn out to be inconsistent after formalization. The paradoxes mentioned have been disappoin ...
An analytic approach for obtaining maximal entropy OWA operator weights ∗ Robert Full´er
... Additionally, Fuller and Majlender (2001) used Lagrange multipliers on Yager’s OWA equation to derive a polynomial equation, which determines the optimal weighting vector under maximal entropy (ME-OWA operator). The proposed approach thus determines the optimal weighting vector under maximal entropy ...
... Additionally, Fuller and Majlender (2001) used Lagrange multipliers on Yager’s OWA equation to derive a polynomial equation, which determines the optimal weighting vector under maximal entropy (ME-OWA operator). The proposed approach thus determines the optimal weighting vector under maximal entropy ...
Higher Order Logic - Indiana University
... 7 Theorem 2.3.1 shows that a particular countable structure, that of the natural numbers, is characterized up to isomorphism by its second order theory. A natural question is whether every countable structure is so characterized. [Ajtai, 1979] (reported in [Shapiro, 1991, Section 6.6.4], who attribu ...
... 7 Theorem 2.3.1 shows that a particular countable structure, that of the natural numbers, is characterized up to isomorphism by its second order theory. A natural question is whether every countable structure is so characterized. [Ajtai, 1979] (reported in [Shapiro, 1991, Section 6.6.4], who attribu ...
Higher Order Logic - Theory and Logic Group
... 7 Theorem 2.3.1 shows that a particular countable structure, that of the natural numbers, is characterized up to isomorphism by its second order theory. A natural question is whether every countable structure is so characterized. [Ajtai, 1979] (reported in [Shapiro, 1991, Section 6.6.4], who attribu ...
... 7 Theorem 2.3.1 shows that a particular countable structure, that of the natural numbers, is characterized up to isomorphism by its second order theory. A natural question is whether every countable structure is so characterized. [Ajtai, 1979] (reported in [Shapiro, 1991, Section 6.6.4], who attribu ...
The Herbrand Manifesto
... This allows us to give complete definitions to things that cannot be completely defined with Tarskian Semantics. We have already seen Peano arithmetic. It turns out that, under Herbrand semantics, we can also define some other useful concepts that are not definable with Tarskian semantics, and we ca ...
... This allows us to give complete definitions to things that cannot be completely defined with Tarskian Semantics. We have already seen Peano arithmetic. It turns out that, under Herbrand semantics, we can also define some other useful concepts that are not definable with Tarskian semantics, and we ca ...
x - Homepages | The University of Aberdeen
... Applications of Predicate Logic It is one of the most-used formal notations for writing mathematical definitions, axioms, and theorems. For example, in linear algebra, a partial order is introduced saying that a relation R is reflexive and transitive – and these notions are defined using predicate l ...
... Applications of Predicate Logic It is one of the most-used formal notations for writing mathematical definitions, axioms, and theorems. For example, in linear algebra, a partial order is introduced saying that a relation R is reflexive and transitive – and these notions are defined using predicate l ...
Artificial Intelligence
... then we get 6 to 7 we get 13, then we add 8 to 13 we get 21 and finally if we’ll add 10 to 21 we’ll get 31 as the answer. Again answering the question requires a little bit intelligence. The characteristic of intelligence comes in when we try to solve something, we check various ways to solve it, we ...
... then we get 6 to 7 we get 13, then we add 8 to 13 we get 21 and finally if we’ll add 10 to 21 we’ll get 31 as the answer. Again answering the question requires a little bit intelligence. The characteristic of intelligence comes in when we try to solve something, we check various ways to solve it, we ...
Special Issue on Semantic Web Meets
... for fast data storage/access. Nowadays, data storage has become extremely cheap. According to Kevin Kelly of Wired magazine, for less than $600, we can purchase a disk drive with the capacity to store all of the world’s music.With cloud computing technology, data access will become even cheaper and ...
... for fast data storage/access. Nowadays, data storage has become extremely cheap. According to Kevin Kelly of Wired magazine, for less than $600, we can purchase a disk drive with the capacity to store all of the world’s music.With cloud computing technology, data access will become even cheaper and ...
Modal Logic for Artificial Intelligence
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
... is valid, regardless of the sentences we use in the place of A and B. The only items that need to be fixed are ‘or’ and ‘not’ in this case. If we would replace ‘not’ by ‘maybe’, then the argument would not be valid anymore. We call ‘or’ and ‘not’ logical constants. Together with ‘and’, ‘if . . . the ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
Teach Yourself Logic 2017: 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 ...
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.