On the Notion of Coherence in Fuzzy Answer Set Semantics
... lack of information is not the reason of this contradiction. Therefore the only possibility to obtain a non contradictory2 interpretation is by removing information. Thus if we obtain an incoherent interpretation as least fixpoint of a logic program, it has been due to an excess of information in th ...
... lack of information is not the reason of this contradiction. Therefore the only possibility to obtain a non contradictory2 interpretation is by removing information. Thus if we obtain an incoherent interpretation as least fixpoint of a logic program, it has been due to an excess of information in th ...
Argumentative Approaches to Reasoning with Maximal Consistency
... A well-established method for handling inconsistencies in a given set of premises is to consider its maximally consistent subsets (MCS). Following the influential work of Rescher and Manor (1970) this approach has gained a considerable popularity and was applied in many AI-related areas. The goal of ...
... A well-established method for handling inconsistencies in a given set of premises is to consider its maximally consistent subsets (MCS). Following the influential work of Rescher and Manor (1970) this approach has gained a considerable popularity and was applied in many AI-related areas. The goal of ...
pdf file
... Theorem 1 assures that all default theories have a maximal extension (different
from L as long as W is consistent). The proof is
just an adaptation of Lindenbaum theorem that
asserts that any consistent set of first-order
formulae can be extended to a maximal
consistent set.
...
... Theorem 1 assures that all default theories
Handling Exceptions in nonmonotonic reasoning
... Notice that g2 leads to an exception to g1 , hence these two generalizations are incompatible. There is no consensus in the AI community about the outcoming of this very simple defeasible axiomatic basis. Some argue that only g2 should be derived and others argue for splitting the expansions: one ap ...
... Notice that g2 leads to an exception to g1 , hence these two generalizations are incompatible. There is no consensus in the AI community about the outcoming of this very simple defeasible axiomatic basis. Some argue that only g2 should be derived and others argue for splitting the expansions: one ap ...
Constraint Propagation as a Proof System
... by using ordered binary decision diagrams (OBDDs) as our representation class for constraints. OBDDs possess many desirable algorithmic properties and have been used successfully in many areas, most notably in formal verification (see [Bry92,BCM 92]). We compare the strength of refutations by OBDDs ...
... by using ordered binary decision diagrams (OBDDs) as our representation class for constraints. OBDDs possess many desirable algorithmic properties and have been used successfully in many areas, most notably in formal verification (see [Bry92,BCM 92]). We compare the strength of refutations by OBDDs ...
The Surprise Examination Paradox and the Second Incompleteness
... Berry’s paradox: consider the expression “the smallest positive integer not definable in under eleven words.” This expression defines that integer in under eleven words. To formalize Berry’s paradox, Chaitin uses the notion of Kolmogorov complexity. The Kolmogorov complexity K(x) of an integer x is ...
... Berry’s paradox: consider the expression “the smallest positive integer not definable in under eleven words.” This expression defines that integer in under eleven words. To formalize Berry’s paradox, Chaitin uses the notion of Kolmogorov complexity. The Kolmogorov complexity K(x) of an integer x is ...
Specification Predicates with Explicit Dependency Information
... Richard Bubel1 , Reiner Hähnle1 , and Peter H. Schmitt2 ...
... Richard Bubel1 , Reiner Hähnle1 , and Peter H. Schmitt2 ...
Digital Systems Topic 2: Logic Gates and Families: Definitions and Characteristics
... • If either A OR B goes high: – Transistor on stage 1 turns on (saturated), turns off stage 2 transistor, and output goes high ...
... • If either A OR B goes high: – Transistor on stage 1 turns on (saturated), turns off stage 2 transistor, and output goes high ...
Formal systems of fuzzy logic and their fragments∗
... prove our results in as general form as possible so they are surely applicable to much wider classes of logics as well. It turned out that these prominent fuzzy logics are natural expansions of the famous logic BCK. This logic was introduced by C.A. Meredith (see e.g. [48, 40]) as a pure implication ...
... prove our results in as general form as possible so they are surely applicable to much wider classes of logics as well. It turned out that these prominent fuzzy logics are natural expansions of the famous logic BCK. This logic was introduced by C.A. Meredith (see e.g. [48, 40]) as a pure implication ...
Weyl`s Predicative Classical Mathematics as a Logic
... rules now mirror the rules of deduction of classical logic, such as the ‘freeze’ and ‘unfreeze’ operations of the λµ-calculus [Parigot 1992]. However, doing so allows new objects to be formed in the datatypes. There have also been several formalisations of classical proofs which used an intuitionist ...
... rules now mirror the rules of deduction of classical logic, such as the ‘freeze’ and ‘unfreeze’ operations of the λµ-calculus [Parigot 1992]. However, doing so allows new objects to be formed in the datatypes. There have also been several formalisations of classical proofs which used an intuitionist ...
An Introduction to Proof Theory - UCSD Mathematics
... In practice, social proofs and formal proofs are very closely related. Firstly, a formal proof can serve as a social proof (although it may be very tedious and unintuitive) provided it is formalized in a proof system whose validity is trusted. Secondly, the standards for social proofs are sufficient ...
... In practice, social proofs and formal proofs are very closely related. Firstly, a formal proof can serve as a social proof (although it may be very tedious and unintuitive) provided it is formalized in a proof system whose validity is trusted. Secondly, the standards for social proofs are sufficient ...
EN 1215661
... energy loss in the form of dissipated heat. In ideal adiabatic logic, each charge could be recycled (reused) an infinite number of times. So that a significant power dissipation reduction would be possible. In real-time computing, such ideal process cannot be achieved because of the presence of diss ...
... energy loss in the form of dissipated heat. In ideal adiabatic logic, each charge could be recycled (reused) an infinite number of times. So that a significant power dissipation reduction would be possible. In real-time computing, such ideal process cannot be achieved because of the presence of diss ...
Relevant deduction
... in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical ...
... in various fields of analytic philosophy. In distinction to relevance logics, this approach does not replace classical logic by a new one, but distinguishes between relevance and validity. It is argued that irrelevant arguments are, although formally valid, nonsensical and even harmful in practical ...
Logic and Existential Commitment
... non-logical elements. The structure of a sentence determines how its unstructured parts (or elements) may be used in relation to one another and how the truth or falsity of the sentence depends upon such a coordinated use of elements. A possible use will be any coordinated use of the elements of a s ...
... non-logical elements. The structure of a sentence determines how its unstructured parts (or elements) may be used in relation to one another and how the truth or falsity of the sentence depends upon such a coordinated use of elements. A possible use will be any coordinated use of the elements of a s ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.