beliefrevision , epistemicconditionals andtheramseytest
... In view of Gärdenfors’ impossibility result, one can do as Levi (1988) suggests: deny that epistemic conditionals have truth-values and for this reason deny that they can be members of belief sets. Alternatively, one can continue to treat epistemic conditionals as possible members of belief sets and ...
... In view of Gärdenfors’ impossibility result, one can do as Levi (1988) suggests: deny that epistemic conditionals have truth-values and for this reason deny that they can be members of belief sets. Alternatively, one can continue to treat epistemic conditionals as possible members of belief sets and ...
Model Theory of Second Order Logic
... be the set of A ⊆ N with A∆G finite. We show that M = (ω ∪ F G , ω, <, E), where nEx ⇐⇒ n ∈ X , is not characterizable by a second order theory. Let M0 = (ω ∪ F −G , ω, <, E). Since M M0 , it suffices to prove that M and M0 are second order equivalent. In fact more is true: If Φ(x) is any formula ...
... be the set of A ⊆ N with A∆G finite. We show that M = (ω ∪ F G , ω, <, E), where nEx ⇐⇒ n ∈ X , is not characterizable by a second order theory. Let M0 = (ω ∪ F −G , ω, <, E). Since M M0 , it suffices to prove that M and M0 are second order equivalent. In fact more is true: If Φ(x) is any formula ...
quine`s argument from despair
... beliefs about the world, especially our well-established scientific theories, from basic observation statements. The conceptual project, on the other hand, is concerned with meaning and aims at translating our scientific concepts in sensory terms. The two projects are connected: if one succeeds in d ...
... beliefs about the world, especially our well-established scientific theories, from basic observation statements. The conceptual project, on the other hand, is concerned with meaning and aims at translating our scientific concepts in sensory terms. The two projects are connected: if one succeeds in d ...
Chapter 2 Propositional Logic
... wff. That’s why we use the metalinguistic variables “φ” and “ψ”.2 The practice of using variables to express generality is familiar; we can say, for example, “for any integer n, if n is even, then n + 2 is even as well”. Just as “n” here is a variable for numbers, metalinguistic variables are variab ...
... wff. That’s why we use the metalinguistic variables “φ” and “ψ”.2 The practice of using variables to express generality is familiar; we can say, for example, “for any integer n, if n is even, then n + 2 is even as well”. Just as “n” here is a variable for numbers, metalinguistic variables are variab ...
Reasoning in Description Logics with a Concrete Domain in the
... the set of concrete domain literals in I is not D-satisfiable. Then, I contains a minimal connected D-constraint S = {di (ti )}. By definition of I, literals in S were produced by some Ei = Ci ∨di (ti ) ∈ N , where Ei is false in IEi . For any i, since di (ti ) is strictly maximal in Ci , Ci is fals ...
... the set of concrete domain literals in I is not D-satisfiable. Then, I contains a minimal connected D-constraint S = {di (ti )}. By definition of I, literals in S were produced by some Ei = Ci ∨di (ti ) ∈ N , where Ei is false in IEi . For any i, since di (ti ) is strictly maximal in Ci , Ci is fals ...
John Nolt – Logics, chp 11-12
... and OO is true if and only if O is true in at least one possible world. The operators '•' and ' 0 ' are thus akin, respectively, to universal and existential quantifiers over a domain of possible worlds. So, for example, to say that it is necessary that 2 + 2 = 4 is to say that in all possible world ...
... and OO is true if and only if O is true in at least one possible world. The operators '•' and ' 0 ' are thus akin, respectively, to universal and existential quantifiers over a domain of possible worlds. So, for example, to say that it is necessary that 2 + 2 = 4 is to say that in all possible world ...
Essence and Modality The Quintessence of Husserl`s Theory Kevin
... bloßen Spiele? […] Wenn man auf die Bedeutungen zurückgehen wollte, so fänden die Regeln in eben diesen Bedeutungen ihre Begründung” (Frege 1903 II, § 90; cf. ...
... bloßen Spiele? […] Wenn man auf die Bedeutungen zurückgehen wollte, so fänden die Regeln in eben diesen Bedeutungen ihre Begründung” (Frege 1903 II, § 90; cf. ...
Many-Valued Models
... • Reasoning with truth-value gaps In 1938 Ł ukasiewicz delivered a lecture to the Circle of Scientists in Warsaw, Genesis of three-valued logic. Ł ukasiewicz considered the discovery of manyvalued logics as important as of non-Euclidean geometry, and thought that they make possible “other ways of s ...
... • Reasoning with truth-value gaps In 1938 Ł ukasiewicz delivered a lecture to the Circle of Scientists in Warsaw, Genesis of three-valued logic. Ł ukasiewicz considered the discovery of manyvalued logics as important as of non-Euclidean geometry, and thought that they make possible “other ways of s ...
Turner`s Logic of Universal Causation, Propositional Logic, and
... where I ∗ |= aφ for corresponding φ ∈ AtomC (T ). Note that, {I, J} |= φ, I |= l1 ∨ · · · ∨ ln and J |= l1 ∨ · · · ∨ ln . Consider the case, for each literal l ∈ {l1 , . . . , ln }, ¯l ∈ I implies ¯l ∈ I ∩ J, then there exists literal l ∈ {l1 , . . . , ln } and l ∈ J such that l ∈ I (if not, ¯l ∈ I ...
... where I ∗ |= aφ for corresponding φ ∈ AtomC (T ). Note that, {I, J} |= φ, I |= l1 ∨ · · · ∨ ln and J |= l1 ∨ · · · ∨ ln . Consider the case, for each literal l ∈ {l1 , . . . , ln }, ¯l ∈ I implies ¯l ∈ I ∩ J, then there exists literal l ∈ {l1 , . . . , ln } and l ∈ J such that l ∈ I (if not, ¯l ∈ I ...
John L. Pollock
... and concepts that are indispensable for advanced work in philosophy and to do so in a way that conveys the important concepts and techniques without becoming embroiled in unnecessary technical details. The most valuable technical tools are those provided by set theory and the predicate calculus. Kno ...
... and concepts that are indispensable for advanced work in philosophy and to do so in a way that conveys the important concepts and techniques without becoming embroiled in unnecessary technical details. The most valuable technical tools are those provided by set theory and the predicate calculus. Kno ...
PDF
... Choose r = 0, prove 02≤0 ∧ 0<(0+1)2 using standard arithmetic – Step case: assume ∃rn r2≤n ∧ n<(rn+1)2 and prove ∃r r 2≤n+1 ∧ n+1<(r+1)2 ...
... Choose r = 0, prove 02≤0 ∧ 0<(0+1)2 using standard arithmetic – Step case: assume ∃rn r2≤n ∧ n<(rn+1)2 and prove ∃r r 2≤n+1 ∧ n+1<(r+1)2 ...
