full text (.pdf)
... Propositional Hoare logic (PHL) consists of atomic proposition and program symbols, the usual propositional connectives, while program constructs, and PCAs built from these. Atomic programs are interpreted as binary relations on a set M and atomic propositions are interpreted as subsets of M. The de ...
... Propositional Hoare logic (PHL) consists of atomic proposition and program symbols, the usual propositional connectives, while program constructs, and PCAs built from these. Atomic programs are interpreted as binary relations on a set M and atomic propositions are interpreted as subsets of M. The de ...
- Free Documents
... formula . Note that L will mean that is derivable from using the axioms and rules of L including Necessitation but not substitution. This means that L is equivalent to L . We say is interderivable with quot and write for the conjunction of L and L . Note that this implies that always . We reserve th ...
... formula . Note that L will mean that is derivable from using the axioms and rules of L including Necessitation but not substitution. This means that L is equivalent to L . We say is interderivable with quot and write for the conjunction of L and L . Note that this implies that always . We reserve th ...
Godel`s Incompleteness Theorem
... • Formal proofs demonstrate consequence, but not non-consequence • Formal proof systems themselves aren’t systematic • But maybe a systematic method can nevertheless be created on the basis of formal logic? – Truth trees are systematic … and can demonstrate consequence as well as non-consequence. Co ...
... • Formal proofs demonstrate consequence, but not non-consequence • Formal proof systems themselves aren’t systematic • But maybe a systematic method can nevertheless be created on the basis of formal logic? – Truth trees are systematic … and can demonstrate consequence as well as non-consequence. Co ...
pdf
... If a first-order formula X is valid, then X the there is an atomically closed tableau for F X. ...
... If a first-order formula X is valid, then X the there is an atomically closed tableau for F X. ...
A modal perspective on monadic second
... Gr Gr Define binary relations S1 and S2 such that S1Gr contains exactly the n n pairs of type ((i, j), (i + 1, j)) ∈ Dm × Dm and S2Gr exactly the pairs of n n n , S1Gr , S2Gr ), type ((i, j), (i, j + 1)) ∈ Dm × Dm . A structure Gr = (Dm Gr Gr n where m, n ∈ N≥1 , is called a grid. Grid Gr = (Dm , S1 ...
... Gr Gr Define binary relations S1 and S2 such that S1Gr contains exactly the n n pairs of type ((i, j), (i + 1, j)) ∈ Dm × Dm and S2Gr exactly the pairs of n n n , S1Gr , S2Gr ), type ((i, j), (i, j + 1)) ∈ Dm × Dm . A structure Gr = (Dm Gr Gr n where m, n ∈ N≥1 , is called a grid. Grid Gr = (Dm , S1 ...
Semi-constr. theories - Stanford Mathematics
... fx = 0 → E0f = 0 and E0f = 0 → x (fx = 0). The first of these is automatically taken care of, and the N-interpretation of the second is taken care of by the verification of MP, but in order to get its further D-interpretation we need to have a functional X which satisfies E0f = 0 → f(Xf) = 0, and he ...
... fx = 0 → E0f = 0 and E0f = 0 → x (fx = 0). The first of these is automatically taken care of, and the N-interpretation of the second is taken care of by the verification of MP, but in order to get its further D-interpretation we need to have a functional X which satisfies E0f = 0 → f(Xf) = 0, and he ...
Kripke completeness revisited
... Kripke’s proof was criticized in a review by Kaplan as lacking in rigor and as making excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for class ...
... Kripke’s proof was criticized in a review by Kaplan as lacking in rigor and as making excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for class ...
classden
... continuous functions from D to D. This guarantees that any object d ∈ D is also a function d : D → D and hence that it is meaningful to talk about d(d). Scott domains thus support the interpretation of self-application and in fact are essential for the interpretation of functional languages which ar ...
... continuous functions from D to D. This guarantees that any object d ∈ D is also a function d : D → D and hence that it is meaningful to talk about d(d). Scott domains thus support the interpretation of self-application and in fact are essential for the interpretation of functional languages which ar ...
CA208ex1 - DCU School of Computing
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
Restricted notions of provability by induction
... to develop algorithms that find proofs by induction and to implement them efficiently. This subject is characterized by a great variety of different methods (and systems implementing these methods), for example, rippling [6], theory exploration [9], integration into a superposition prover [18, 24], ...
... to develop algorithms that find proofs by induction and to implement them efficiently. This subject is characterized by a great variety of different methods (and systems implementing these methods), for example, rippling [6], theory exploration [9], integration into a superposition prover [18, 24], ...
predicate
... • 1,…,n ⊨ holds iff 1,…,n ⊢ is valid • In particular, ⊨ , a tautology, ⊢ is valid. I.E. is a tautology iff is provable • Soundness – you can not prove things that are not true in the truth table sense • Completeness – you can prove anything that is true in the truth table sense ...
... • 1,…,n ⊨ holds iff 1,…,n ⊢ is valid • In particular, ⊨ , a tautology, ⊢ is valid. I.E. is a tautology iff is provable • Soundness – you can not prove things that are not true in the truth table sense • Completeness – you can prove anything that is true in the truth table sense ...
Abstract for ‘Consequentialism’ 1 Inferentialism vs referentialism David Ripley
... this sense, is adopted by [Restall, 2009] and [Ripley, 2013]. Both of these papers claim that the views they put forward are inferentialist, but this is not in fact the case, if inferentialism is understood as above; neither paper has much at all to do with legitimate inference, except insofar as th ...
... this sense, is adopted by [Restall, 2009] and [Ripley, 2013]. Both of these papers claim that the views they put forward are inferentialist, but this is not in fact the case, if inferentialism is understood as above; neither paper has much at all to do with legitimate inference, except insofar as th ...