The Foundations
... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...
... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...
notes
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
Non-Classical Logic
... We might here present a traditional deductive system for classical propositional logic. However, I assume you already familiar with at least one such system, whether it is a natural deduction system or axiom system. All such standard systems are equivalent and yield the same results. We write: ∆`A ...
... We might here present a traditional deductive system for classical propositional logic. However, I assume you already familiar with at least one such system, whether it is a natural deduction system or axiom system. All such standard systems are equivalent and yield the same results. We write: ∆`A ...
Dependence Logic
... D. We will later in Section 1.6 recover independence friendly logic as a fragment of dependence logic. In first order logic the meaning of a formula is derived from the concept of an assignment satisfying the formula. In dependence logic the meaning of a formula is based on the concept of a team bei ...
... D. We will later in Section 1.6 recover independence friendly logic as a fragment of dependence logic. In first order logic the meaning of a formula is derived from the concept of an assignment satisfying the formula. In dependence logic the meaning of a formula is based on the concept of a team bei ...
pdf
... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
... However, in many seemingly analogous cases we do have termination nevertheless, e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s f ...
COOL MATH! - James Tanton
... five-sided equilateral lattice polygon? A six-sided one? For which values N is it possible to draw an equilateral lattice N -gon? Giving half the answers away, the following diagram shows that it is possible to draw an equilateral lattice N -gon for any even number N > 2 . (This picture makes use of ...
... five-sided equilateral lattice polygon? A six-sided one? For which values N is it possible to draw an equilateral lattice N -gon? Giving half the answers away, the following diagram shows that it is possible to draw an equilateral lattice N -gon for any even number N > 2 . (This picture makes use of ...
Constraint Propagation as a Proof System
... new formalism, CSP proofs become purely syntactical objects, closer to their counterparts in propositional logic. As a case study, we investigate the proof system obtained by using ordered binary decision diagrams (OBDDs) as our representation class for constraints. OBDDs possess many desirable algo ...
... new formalism, CSP proofs become purely syntactical objects, closer to their counterparts in propositional logic. As a case study, we investigate the proof system obtained by using ordered binary decision diagrams (OBDDs) as our representation class for constraints. OBDDs possess many desirable algo ...
Views: Compositional Reasoning for Concurrent Programs
... may be consistently composed only if they describe disjoint sets of variables, which each thread can be seen to own. Note that, since heap locations may be aliased by multiple variables, it is not in general permissible to update their types. However, a type system may include unique reference types ...
... may be consistently composed only if they describe disjoint sets of variables, which each thread can be seen to own. Note that, since heap locations may be aliased by multiple variables, it is not in general permissible to update their types. However, a type system may include unique reference types ...
LOWNESS NOTIONS, MEASURE AND DOMINATION
... and s ∈ ω, X[s] denotes the string hX(0), X(1), . . . , X(s − 1)i. For Y ⊆ 2<ω , [Y ] denotes the open class in 2ω of all X such that ∃σ ∈ Y (σ v X). If Z ⊆ 2ω , then Z c = 2ω \ Z. Finally, if M is any machine (viewed as defining a partial function from 2<ω to 2<ω ), then dom(M ) denotes the set of ...
... and s ∈ ω, X[s] denotes the string hX(0), X(1), . . . , X(s − 1)i. For Y ⊆ 2<ω , [Y ] denotes the open class in 2ω of all X such that ∃σ ∈ Y (σ v X). If Z ⊆ 2ω , then Z c = 2ω \ Z. Finally, if M is any machine (viewed as defining a partial function from 2<ω to 2<ω ), then dom(M ) denotes the set of ...
Classical Propositional Logic
... How to do it in the first place: suitable calculi? How to do it efficiently: search space control? How to do it optimally: reasoning support for specific theories like equality and arithmetic? ...
... How to do it in the first place: suitable calculi? How to do it efficiently: search space control? How to do it optimally: reasoning support for specific theories like equality and arithmetic? ...
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction
... We assume that the both sets A and F are enumerable, i.e. we will deal here with enumerable languages only. Given a set F of well formed formulas, of the language L, we often extend this set (and hence the language L to some set E of expressions build out of the language L, and some additional symbo ...
... We assume that the both sets A and F are enumerable, i.e. we will deal here with enumerable languages only. Given a set F of well formed formulas, of the language L, we often extend this set (and hence the language L to some set E of expressions build out of the language L, and some additional symbo ...
Heyting-valued interpretations for Constructive Set Theory
... formal topology and constructive set theories analogous to the one existing between locale theory and intuitionistic set theories. We do so by investigating Heyting-valued interpretations for the Constructive Zermelo-Frankel set theory, CZF [6]. The study of Heyting-valued interpretations reveals ma ...
... formal topology and constructive set theories analogous to the one existing between locale theory and intuitionistic set theories. We do so by investigating Heyting-valued interpretations for the Constructive Zermelo-Frankel set theory, CZF [6]. The study of Heyting-valued interpretations reveals ma ...
Scattered Sentences have Few Separable Randomizations
... connectives, and quantifiers. A separable randomization of an Lω1 ω -sentence ϕ is a separable randomization whose completion satisfies µ(JϕK) = 1. Intuitively, in a separable randomization of ϕ, a random element is obtained by randomly picking an element of a random countable model of ϕ, with respe ...
... connectives, and quantifiers. A separable randomization of an Lω1 ω -sentence ϕ is a separable randomization whose completion satisfies µ(JϕK) = 1. Intuitively, in a separable randomization of ϕ, a random element is obtained by randomly picking an element of a random countable model of ϕ, with respe ...
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Alignment and Survey - Oxford Particle Physics home
... – Q: What kind of symmetries can you impose on a field theory and still have non-zero scattering? – Coleman and Mandula say there are only 2 classes of conserved quantities: • External – Poincare’ symmetry (Lorentz invariance) • Energy-momentum conservation • Angular momentum conservation ...
... – Q: What kind of symmetries can you impose on a field theory and still have non-zero scattering? – Coleman and Mandula say there are only 2 classes of conserved quantities: • External – Poincare’ symmetry (Lorentz invariance) • Energy-momentum conservation • Angular momentum conservation ...
Annals of Pure and Applied Logic Commutative integral bounded
... doi:10.1016/j.apal.2009.05.008 ...
... doi:10.1016/j.apal.2009.05.008 ...
The Dedekind Reals in Abstract Stone Duality
... reference to the real line in Sections 3, 5 and 7. All maps between these spaces are continuous, not as a theorem but by definition — the calculus simply never introduces discontinuous functions. Maps are defined by a (form of) λ-calculus, so we sometimes refer to spaces as types. Statements in the ...
... reference to the real line in Sections 3, 5 and 7. All maps between these spaces are continuous, not as a theorem but by definition — the calculus simply never introduces discontinuous functions. Maps are defined by a (form of) λ-calculus, so we sometimes refer to spaces as types. Statements in the ...
Combining Paraconsistent Logic with Argumentation
... itself; otherwise it is conflicting. A set is admissible if it is conflict-free and defends itself by attacking each argument attacking S. Extensions are admissible sets with some additional properties. They can be defined according to the function F : 2A → 2A such that F (S) = {A|A A is defended b ...
... itself; otherwise it is conflicting. A set is admissible if it is conflict-free and defends itself by attacking each argument attacking S. Extensions are admissible sets with some additional properties. They can be defined according to the function F : 2A → 2A such that F (S) = {A|A A is defended b ...
Boolean Connectives and Formal Proofs - FB3
... rule allows you to introduce, for any name (or complex term) the proof, the assertion n = n. You are allowed to do this at an proof, and need not cite any earlier step as justification. We w our statement of this rule in the following way: Identity Introduction (= Intro): . n=n ...
... rule allows you to introduce, for any name (or complex term) the proof, the assertion n = n. You are allowed to do this at an proof, and need not cite any earlier step as justification. We w our statement of this rule in the following way: Identity Introduction (= Intro): . n=n ...
NONSTANDARD MODELS IN RECURSION THEORY
... of PA and recursion theory in §3. In the final section, we discuss subsystems of second order arithmetic and Ramsey type combinatorial principles. We avoid detailed proofs of any theorem, but provide sketches of the key ideas where appropriate. 2. Fragments of Peano Arithmetic and their models The l ...
... of PA and recursion theory in §3. In the final section, we discuss subsystems of second order arithmetic and Ramsey type combinatorial principles. We avoid detailed proofs of any theorem, but provide sketches of the key ideas where appropriate. 2. Fragments of Peano Arithmetic and their models The l ...