HOARE`S LOGIC AND PEANO`S ARITHMETIC
... Induction scheme : for each assertion p E L, containing free variable X,the foilowingisanaxiom[p(O)AVx l(p(x)+p(x+l))]+Vx *p(x), Thus, we may observe that equations (3)-(6) alone define N under initial algebra semantics and so we may consider (1) and (2) as additions, making a first refinement of th ...
... Induction scheme : for each assertion p E L, containing free variable X,the foilowingisanaxiom[p(O)AVx l(p(x)+p(x+l))]+Vx *p(x), Thus, we may observe that equations (3)-(6) alone define N under initial algebra semantics and so we may consider (1) and (2) as additions, making a first refinement of th ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... as least fixpoint of a logic program, it has been due to an excess of information in the program (possibly erroneous information). As a result, rejecting noncoherent interpretations seems convenient as well. An important remark is that coherence can be interpreted with an empirical sense and that th ...
... as least fixpoint of a logic program, it has been due to an excess of information in the program (possibly erroneous information). As a result, rejecting noncoherent interpretations seems convenient as well. An important remark is that coherence can be interpreted with an empirical sense and that th ...
Modus Ponens Defended
... his paper. Katz [1999] even expresses skepticism about the possibility of such a semantics: I find it doubtful that there is any consistent interpretation of the conditionals occurring in McGee’s example, truth functional or otherwise, which will make the premises true and the conclusion false. (p. ...
... his paper. Katz [1999] even expresses skepticism about the possibility of such a semantics: I find it doubtful that there is any consistent interpretation of the conditionals occurring in McGee’s example, truth functional or otherwise, which will make the premises true and the conclusion false. (p. ...
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
Partial Grounded Fixpoints
... We start by giving the central definition of this text, namely the notion of A-groundedness. Definition 3.1. Let A be an approximator of O. A point (x, y) ∈ Lc is A-grounded if for every v ∈ L with A(x ∧ v, y ∧ v)2 ≤ v, also y ≤ v. The definition of this concept is a direct generalisation of grounde ...
... We start by giving the central definition of this text, namely the notion of A-groundedness. Definition 3.1. Let A be an approximator of O. A point (x, y) ∈ Lc is A-grounded if for every v ∈ L with A(x ∧ v, y ∧ v)2 ≤ v, also y ≤ v. The definition of this concept is a direct generalisation of grounde ...
