Harmony, Normality and Stability
... deductions in such a way that these ‘detours’ are avoided. Applying the reduction procedures should always turn deductions into new deductions. Trivial as this observation may sound, it shows that the point of having harmonious rules is not that they exhibit some feature independently of any logic i ...
... deductions in such a way that these ‘detours’ are avoided. Applying the reduction procedures should always turn deductions into new deductions. Trivial as this observation may sound, it shows that the point of having harmonious rules is not that they exhibit some feature independently of any logic i ...
Landau`s Fermi Liquid Theory
... The concept of a Fermi Liquid describes (strongly) interacting fermions using concepts that naively would only be applicable to a very weakly interacting gas. That this is at all possible makes Fermi Liquid theory a very versatile, but at the same time its very success is puzzling. Fermi Liquid theo ...
... The concept of a Fermi Liquid describes (strongly) interacting fermions using concepts that naively would only be applicable to a very weakly interacting gas. That this is at all possible makes Fermi Liquid theory a very versatile, but at the same time its very success is puzzling. Fermi Liquid theo ...
Frank Wilczek 1 Selected Publications of Frank Wilczek, with Brief Commentary
... raising the scale without grossly modifying the structure. In Item 58 we showed how supersymmetric models based on the group SO(10) (or, of course, a larger group) contain a very natural mechanism for lifting the troublesome Higgs color triplet to very high mass, leaving the doublet behind. This is ...
... raising the scale without grossly modifying the structure. In Item 58 we showed how supersymmetric models based on the group SO(10) (or, of course, a larger group) contain a very natural mechanism for lifting the troublesome Higgs color triplet to very high mass, leaving the doublet behind. This is ...
Elements of Finite Model Theory
... enumerable; in other words, completeness fails over finite models. The technique of the proof, based on encoding Turing machine computations as finite structures, was reused by Fagin almost a quarter century later to prove his celebrated result that put the equality sign between the class NP and exist ...
... enumerable; in other words, completeness fails over finite models. The technique of the proof, based on encoding Turing machine computations as finite structures, was reused by Fagin almost a quarter century later to prove his celebrated result that put the equality sign between the class NP and exist ...
An Institution-Independent Generalization of Tarski`s Elementary
... liberal on signature morphisms if the functor Mod(ϕ) has a left adjoint for each signature morphism ϕ. A presentation is a pair (Σ, E), where E ⊆ Sen(Σ). A theory is a presentation (Σ, E) with E closed, i.e., with E • = E. One usually calls “presentation” or “theory” only the set E, and not the whol ...
... liberal on signature morphisms if the functor Mod(ϕ) has a left adjoint for each signature morphism ϕ. A presentation is a pair (Σ, E), where E ⊆ Sen(Σ). A theory is a presentation (Σ, E) with E closed, i.e., with E • = E. One usually calls “presentation” or “theory” only the set E, and not the whol ...
logic, programming and prolog (2ed)
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
Preferences and Unrestricted Rebut
... of the form ϕ1 , . . . , ϕn → ϕ and ϕ1 , . . . , ϕn ⇒ ϕ respectively (where ϕi , ϕ are meta-variables ranging over wff in L), and Rs ∩ Rd = ∅. Rs is assumed to be closed under transposition, i.e., if φ1 , . . . , φn → ψ ∈ Rs , then for i = 1 . . . n, φ1 , . . . , φi−1 , −ψ, φi+1 , . . . , φn → −φi ∈ ...
... of the form ϕ1 , . . . , ϕn → ϕ and ϕ1 , . . . , ϕn ⇒ ϕ respectively (where ϕi , ϕ are meta-variables ranging over wff in L), and Rs ∩ Rd = ∅. Rs is assumed to be closed under transposition, i.e., if φ1 , . . . , φn → ψ ∈ Rs , then for i = 1 . . . n, φ1 , . . . , φi−1 , −ψ, φi+1 , . . . , φn → −φi ∈ ...
Constraint propagation
... There exists a reasoning technique, such that for any theory T and formula F, such that T |= F, the reasoning technique proves T |= F. ...
... There exists a reasoning technique, such that for any theory T and formula F, such that T |= F, the reasoning technique proves T |= F. ...
Slide 1
... Can use effective field theory approach to parametrize ignorance of the new physics Q cannot be much beyond 1 TeV since we know that the Standard Model without a Higgs breaks down at around 1 TeV (WW -> WW violates unitarity) ...
... Can use effective field theory approach to parametrize ignorance of the new physics Q cannot be much beyond 1 TeV since we know that the Standard Model without a Higgs breaks down at around 1 TeV (WW -> WW violates unitarity) ...
KURT GÖDEL - National Academy of Sciences
... is just what comes from substituting {Ao, A,, A2, ...} for A in the immediately preceding statement, and noting that, if a contradiction can be deduced from the formulas A(), A,, A2, ..., only a finite number of them can participate in a given deduction of the contradiction. Thus: Either the formula ...
... is just what comes from substituting {Ao, A,, A2, ...} for A in the immediately preceding statement, and noting that, if a contradiction can be deduced from the formulas A(), A,, A2, ..., only a finite number of them can participate in a given deduction of the contradiction. Thus: Either the formula ...
Chu Spaces - Stanford University
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
Dedukti
... Using product compatibility we can also show that a term has, at most, one type modulo conversion. I Lemma 5 (Uniqueness of Types, Theorem 2.6.34 in [65]). Let Γ be a global context satisfying the product compatibility property. If Γ ` t : T1 and Γ ` t : T2 then T1 ≡βΓ T2 . ...
... Using product compatibility we can also show that a term has, at most, one type modulo conversion. I Lemma 5 (Uniqueness of Types, Theorem 2.6.34 in [65]). Let Γ be a global context satisfying the product compatibility property. If Γ ` t : T1 and Γ ` t : T2 then T1 ≡βΓ T2 . ...
A Logical Framework for Default Reasoning
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
5 model theory of modal logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
Einstein`s quantum theory of the monatomic ideal gas: non
... In order to obtain this factor, Bose divided the six-dimensional phase space of a light quantum into cells of (hyper)volume h3 . He then calculated the probability of a macroscopic state, taking as a microstate only the number of quanta that were contained in each cell, disregarding any information ...
... In order to obtain this factor, Bose divided the six-dimensional phase space of a light quantum into cells of (hyper)volume h3 . He then calculated the probability of a macroscopic state, taking as a microstate only the number of quanta that were contained in each cell, disregarding any information ...
A KE Tableau for a Logic of Formal Inconsistency - IME-USP
... F ◦ X can be in DS, but only if ◦X is a subformula of some other formula in DS. If ◦X is not a subformula of some other formula in DS, neither T ◦ X nor F ◦ X are in DS; 4. if a signed formula S X is in DS, then for any sign S, for any formula X, for all subformulas Y of X and for all n ≥ 0, the sig ...
... F ◦ X can be in DS, but only if ◦X is a subformula of some other formula in DS. If ◦X is not a subformula of some other formula in DS, neither T ◦ X nor F ◦ X are in DS; 4. if a signed formula S X is in DS, then for any sign S, for any formula X, for all subformulas Y of X and for all n ≥ 0, the sig ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
Mathematical Logic
... R(x, y, z), R(t0 , t1 , t2 ), where R is some predicate symbol. Similarly for a unary function symbol with a (typographically) simple argument, so f x for f (x), etc. In this case no confusion will arise. But readability requires that we write in full R(f x, gy, hz), instead of Rf xgyhz. Binary func ...
... R(x, y, z), R(t0 , t1 , t2 ), where R is some predicate symbol. Similarly for a unary function symbol with a (typographically) simple argument, so f x for f (x), etc. In this case no confusion will arise. But readability requires that we write in full R(f x, gy, hz), instead of Rf xgyhz. Binary func ...
George VOUTSADAKIS CATEGORICAL ABSTRACT ALGEBRAIC
... several authors considered the process of coordinatization of various axiomatically defined abstract geometries. Among them were the affine plane geometry, affine plane geometry with the Desargues and Pappus properties, projective plane geometry etc. A classic introductory book to be consulted on th ...
... several authors considered the process of coordinatization of various axiomatically defined abstract geometries. Among them were the affine plane geometry, affine plane geometry with the Desargues and Pappus properties, projective plane geometry etc. A classic introductory book to be consulted on th ...
Gödel Without (Too Many) Tears
... Gödel’s doctoral dissertation, written when he was 23, established the completeness theorem for the first-order predicate calculus (i.e. a standard proof system for first-order logic indeed captures all the semantically valid inferences). Later he would do immensely important work on set theory, as ...
... Gödel’s doctoral dissertation, written when he was 23, established the completeness theorem for the first-order predicate calculus (i.e. a standard proof system for first-order logic indeed captures all the semantically valid inferences). Later he would do immensely important work on set theory, as ...
