An argumentation framework in default logic
... of nonmonotonic reasoning start with a consistent set of premises and provide for ways of deriving plausible but deductively unsound conclusions from them. However, a different approach is allowing the premises to be inconsistent and to prefer some part of the premises if indeed an inconsistency occ ...
... of nonmonotonic reasoning start with a consistent set of premises and provide for ways of deriving plausible but deductively unsound conclusions from them. However, a different approach is allowing the premises to be inconsistent and to prefer some part of the premises if indeed an inconsistency occ ...
x - Loughborough University Intranet
... Pragmatics : Some linguistic forms may lead to referential ambiguities “Tous les nombres ne sont pas pairs” (1) (not all numbers are even) is sometimes interpreted as “Aucun nombre n’est pair” (2) (No number is even), the contrary in Aristotle’ sense. This interpretation is reinforced by the possibi ...
... Pragmatics : Some linguistic forms may lead to referential ambiguities “Tous les nombres ne sont pas pairs” (1) (not all numbers are even) is sometimes interpreted as “Aucun nombre n’est pair” (2) (No number is even), the contrary in Aristotle’ sense. This interpretation is reinforced by the possibi ...
Default Logic (Reiter) - Department of Computing
... • α follows from (D, S W ) by ‘brave’/‘credulous’ reasoning when α in any extension of (D, W ): α ∈ ext(D, W ); • α follows from (D, T W ) by ‘cautious’/‘sceptical’ reasoning when α in all extensions of (D, W ): α ∈ ext(D, W ). ...
... • α follows from (D, S W ) by ‘brave’/‘credulous’ reasoning when α in any extension of (D, W ): α ∈ ext(D, W ); • α follows from (D, T W ) by ‘cautious’/‘sceptical’ reasoning when α in all extensions of (D, W ): α ∈ ext(D, W ). ...
Theories and uses of context in knowledge representation and
... Interestingly enough, KRR seems to share this intuition with other related areas. Two examples will illustrate this “family resemblance”. Sperber and Wilson, in their book on relevance (1986:15), express a similar intuition from a psycholinguistic perspective: “The set of premises used in interpreti ...
... Interestingly enough, KRR seems to share this intuition with other related areas. Two examples will illustrate this “family resemblance”. Sperber and Wilson, in their book on relevance (1986:15), express a similar intuition from a psycholinguistic perspective: “The set of premises used in interpreti ...
- Free Documents
... MON X def X X X e X x y z X x y z x y z x X e x x x e e The type former is a generalisation of the cartesian product to dependent types and corresponds under the propositionsastypes analogy to existential quanti cation. An object of the above generalised signature thus consists of an object of type ...
... MON X def X X X e X x y z X x y z x y z x X e x x x e e The type former is a generalisation of the cartesian product to dependent types and corresponds under the propositionsastypes analogy to existential quanti cation. An object of the above generalised signature thus consists of an object of type ...
pdf
... when viewed as a canonically embedded structure a reduct of a binary random structure. The working hypothesis is that countable, binary, homogeneous, simple and 1-based structures are suciently uncomplicated that it should be possible to work out some sort of rather explicit understanding of ...
... when viewed as a canonically embedded structure a reduct of a binary random structure. The working hypothesis is that countable, binary, homogeneous, simple and 1-based structures are suciently uncomplicated that it should be possible to work out some sort of rather explicit understanding of ...
Higher Order Logic - Theory and Logic Group
... others are omitted altogether, notably most uses of higher order constructs in mathematical practice, in recursion theory, and in computer science. Such choices of topics can not be independent of an author's interests and background. My hope is, though, that the chapter touches on the central issue ...
... others are omitted altogether, notably most uses of higher order constructs in mathematical practice, in recursion theory, and in computer science. Such choices of topics can not be independent of an author's interests and background. My hope is, though, that the chapter touches on the central issue ...
Higher Order Logic - Indiana University
... others are omitted altogether, notably most uses of higher order constructs in mathematical practice, in recursion theory, and in computer science. Such choices of topics can not be independent of an author's interests and background. My hope is, though, that the chapter touches on the central issue ...
... others are omitted altogether, notably most uses of higher order constructs in mathematical practice, in recursion theory, and in computer science. Such choices of topics can not be independent of an author's interests and background. My hope is, though, that the chapter touches on the central issue ...
lecture notes in logic - UCLA Department of Mathematics
... (with ∈ binary) is a signature for universe of sets. (We say a rather than the signature because the “symbols” R, S, +, ∈ etc. are arbitrary.) Definition 1B.2. The alphabet of the first order language with identity FOL(τ ) comprises the symbols in the vocabulary τ and the following, additional symbo ...
... (with ∈ binary) is a signature for universe of sets. (We say a rather than the signature because the “symbols” R, S, +, ∈ etc. are arbitrary.) Definition 1B.2. The alphabet of the first order language with identity FOL(τ ) comprises the symbols in the vocabulary τ and the following, additional symbo ...
Modular Construction of Complete Coalgebraic Logics
... Replacing the unbounded powerset functor by the finite powerset functor in these definitions yields image-finite variants of these two types of systems. The image-finite simple probabilistic automata are called probabilistic transition systems in [12]. Note that all the endofunctors in the previous ...
... Replacing the unbounded powerset functor by the finite powerset functor in these definitions yields image-finite variants of these two types of systems. The image-finite simple probabilistic automata are called probabilistic transition systems in [12]. Note that all the endofunctors in the previous ...
Proof theory for modal logic
... An axiom system for modal logic can be an extension of intuitionistic or classical propositional logic. In the latter, the notions of necessity and possibility are interdefinable by the equivalence 2A ⊃⊂ ¬3¬A. It is seen that necessity and possibility behave analogously to the quantifiers: In one in ...
... An axiom system for modal logic can be an extension of intuitionistic or classical propositional logic. In the latter, the notions of necessity and possibility are interdefinable by the equivalence 2A ⊃⊂ ¬3¬A. It is seen that necessity and possibility behave analogously to the quantifiers: In one in ...
Section 3.3 Equivalence Relation
... Classifying objects and placing similar objects into groups provides a way to organize information and focus attention on the similarities of like objects and not on the dissimilarities of dislike objects. Mathematicians have been classifying objects for millennia. Lines in the plane can be subdivid ...
... Classifying objects and placing similar objects into groups provides a way to organize information and focus attention on the similarities of like objects and not on the dissimilarities of dislike objects. Mathematicians have been classifying objects for millennia. Lines in the plane can be subdivid ...
Syntax and Semantics of Dependent Types
... The -type former is a generalisation of the cartesian product to dependent types and corresponds under the propositions-as-types analogy to existential quanti cation. An object of the above generalised signature thus consists of an object of type (X X ) ! X an object e of type X a proof ...
... The -type former is a generalisation of the cartesian product to dependent types and corresponds under the propositions-as-types analogy to existential quanti cation. An object of the above generalised signature thus consists of an object of type (X X ) ! X an object e of type X a proof ...
Dedukti
... as independent systems. As a consequence, it is difficult to reuse a formal proof developed in an automated or interactive theorem prover based on one of these formalisms in another, without redeveloping it. It is also difficult to combine lemmas proved in different systems: the realm of formal proo ...
... as independent systems. As a consequence, it is difficult to reuse a formal proof developed in an automated or interactive theorem prover based on one of these formalisms in another, without redeveloping it. It is also difficult to combine lemmas proved in different systems: the realm of formal proo ...
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 ...
A causal approach to nonmonotonic reasoning
... will consist in laying down logical foundations for this kind of nonmonotonic reasoning. As we will see, the resulting nonmonotonic formalism will form a most natural and immediate generalization of classical logic that allows for nonmonotonic reasoning. We will try to demonstrate also that the sugg ...
... will consist in laying down logical foundations for this kind of nonmonotonic reasoning. As we will see, the resulting nonmonotonic formalism will form a most natural and immediate generalization of classical logic that allows for nonmonotonic reasoning. We will try to demonstrate also that the sugg ...
Set theory
Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.