cl-ch9
... The terms are sequences of symbols, such as 0 or 0 + 0 or x or x ′′ , that correspond to grammatically well-formed phrases of English of the kind that grammarians call ‘singular noun phrases’. The closed terms are the ones that involve no variables, and the open terms are the ones that involve varia ...
... The terms are sequences of symbols, such as 0 or 0 + 0 or x or x ′′ , that correspond to grammatically well-formed phrases of English of the kind that grammarians call ‘singular noun phrases’. The closed terms are the ones that involve no variables, and the open terms are the ones that involve varia ...
PDF
... Since linear-time formalisms such as LTL can express properties that are not expressible in AFMC (e.g., it follows from the results in Rabin [1970], Muller et al. [1986], and Kupferman et al. [2000], that the LTL formula 3 p is not expressible in AFMC), symbolic model-checking methods become more c ...
... Since linear-time formalisms such as LTL can express properties that are not expressible in AFMC (e.g., it follows from the results in Rabin [1970], Muller et al. [1986], and Kupferman et al. [2000], that the LTL formula 3 p is not expressible in AFMC), symbolic model-checking methods become more c ...
Document
... since physics is fundamentally different from mathematics. However, if we suppose that physics is about individuals, then there is at least a description of the physical world in a formal language. No superior theoretical reason is found not to attempt to formalize physical theories. What is more, n ...
... since physics is fundamentally different from mathematics. However, if we suppose that physics is about individuals, then there is at least a description of the physical world in a formal language. No superior theoretical reason is found not to attempt to formalize physical theories. What is more, n ...
Theory of Neutron -Decay - Fundamental Neutron Physics at NC State
... Thus CP ↔ T violation. Tests of CPT and Lorentz invariance are ongoing. “A search for an annual variation of a daily sidereal modulation of the frequency difference between co-located 129 Xe and 3 He Zeeman masers sets a stringent limit on boost-dependent Lorentz and CPT violation involving the neut ...
... Thus CP ↔ T violation. Tests of CPT and Lorentz invariance are ongoing. “A search for an annual variation of a daily sidereal modulation of the frequency difference between co-located 129 Xe and 3 He Zeeman masers sets a stringent limit on boost-dependent Lorentz and CPT violation involving the neut ...
Lecture Notes
... If, assuming φ, ψ can be proved, then φ ⇒ ψ can be proved. I.e., φ ⊢ ψ implies ⊢ φ ⇒ ψ This does not hold for the logic of knowledge! ...
... If, assuming φ, ψ can be proved, then φ ⇒ ψ can be proved. I.e., φ ⊢ ψ implies ⊢ φ ⇒ ψ This does not hold for the logic of knowledge! ...
Geometric Modal Logic
... acceding to the remark that such an iteration should commit us to far more than is usually acknowledged. Besides, let’s do this within the framework of possible worlds. ...
... acceding to the remark that such an iteration should commit us to far more than is usually acknowledged. Besides, let’s do this within the framework of possible worlds. ...
On the Expressive Power of QLTL⋆
... of LT L). A well-known result is that ω-regular languages can be expressed by X, F operators and existential quantifiers in QLT L [2, 12], which, nevertheless, is almost all we know about the expressive power of QLT L and its fragments besides those of LT L. We do not even know whether several natur ...
... of LT L). A well-known result is that ω-regular languages can be expressed by X, F operators and existential quantifiers in QLT L [2, 12], which, nevertheless, is almost all we know about the expressive power of QLT L and its fragments besides those of LT L. We do not even know whether several natur ...
Polarizing Double-Negation Translations
... This is why we introduce a focused version of the classical sequent calculus. The resulting constraint is that we must decompose the stoup [11,12] formula until it gets removed from the stoup position. Only when the stoup becomes empty, can we apply rules on other formulæ. Definition 4 (Focused sequ ...
... This is why we introduce a focused version of the classical sequent calculus. The resulting constraint is that we must decompose the stoup [11,12] formula until it gets removed from the stoup position. Only when the stoup becomes empty, can we apply rules on other formulæ. Definition 4 (Focused sequ ...
3.6 First-Order Tableau
... Definition 3.7.1 (Unifier). Two terms s and t of the same sort are said to be unifiable if there exists a well-sorted substitution σ so that sσ = tσ, the substitution σ is then called a well-sorted unifier of s and t. The unifier σ is called most general unifier, written σ = mgu(s, t), if any other ...
... Definition 3.7.1 (Unifier). Two terms s and t of the same sort are said to be unifiable if there exists a well-sorted substitution σ so that sσ = tσ, the substitution σ is then called a well-sorted unifier of s and t. The unifier σ is called most general unifier, written σ = mgu(s, t), if any other ...
The Mole - My CCSD
... Note that the NUMBER is always the same, but the MASS is very different! Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?) ...
... Note that the NUMBER is always the same, but the MASS is very different! Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?) ...
Notes on Classical Propositional Logic
... Constructing a truth table for a formula with many propositional letters is a very large task. For more complex logics, the semantics may not even provide an effective method for determining validity. What is often used instead is some notion of formal proof. Axiom systems provide a very common such ...
... Constructing a truth table for a formula with many propositional letters is a very large task. For more complex logics, the semantics may not even provide an effective method for determining validity. What is often used instead is some notion of formal proof. Axiom systems provide a very common such ...
The Mole
... • If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the ...
... • If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles. • If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the ...
Notes on First Order Logic
... 1. x does not occur free in ψ. Then ((∀y)ψ)[x/τ ] is the same as (∀y)ψ. Furthermore s and s[x/τ ] agree on all free variables in (∀y)ψ. By Theorem ??, we have A, s |= (∀y)ψ[x/τ ] iff A, s |= (∀y)ψ iff A, s[x/τ ](∀y)ψ. 2. x does occur free in ψ. Since τ is substitutable for x in (∀y)ψ, according to t ...
... 1. x does not occur free in ψ. Then ((∀y)ψ)[x/τ ] is the same as (∀y)ψ. Furthermore s and s[x/τ ] agree on all free variables in (∀y)ψ. By Theorem ??, we have A, s |= (∀y)ψ[x/τ ] iff A, s |= (∀y)ψ iff A, s[x/τ ](∀y)ψ. 2. x does occur free in ψ. Since τ is substitutable for x in (∀y)ψ, according to t ...
Equality in the Presence of Apartness: An Application of Structural
... the new intuitionistic concepts. We shall here use a uniform notation in which the intuitionistic notion is written with a slash over the classical one, as in a 6= b. The properties of this notion of apartness are, first, irreflexivity ¬ a 6= a, and, secondly, the “splitting” of an apartness a 6= b in ...
... the new intuitionistic concepts. We shall here use a uniform notation in which the intuitionistic notion is written with a slash over the classical one, as in a 6= b. The properties of this notion of apartness are, first, irreflexivity ¬ a 6= a, and, secondly, the “splitting” of an apartness a 6= b in ...
Quantum Field Theory, its Concepts Viewed from a Semiotic
... avoiding technical formulations as far as possible. Various facets are elucidated and distinguished according to differing aims pursued. In section 3 we return in greater detail to the central question: in which way do particles, i.e. the objects observed experimentally, emerge in the theory from th ...
... avoiding technical formulations as far as possible. Various facets are elucidated and distinguished according to differing aims pursued. In section 3 we return in greater detail to the central question: in which way do particles, i.e. the objects observed experimentally, emerge in the theory from th ...
Gödel incompleteness theorems and the limits of their applicability. I
... (based on the Chinese remainder theorem) shows ([1], Theorem VII) that every primitive recursive relation is equivalent (in P ) to some arithmetical formula, that is, a formula of a first-order language in the signature with the constant 0, the functions S, +, and · , and the equality relation. Thus ...
... (based on the Chinese remainder theorem) shows ([1], Theorem VII) that every primitive recursive relation is equivalent (in P ) to some arithmetical formula, that is, a formula of a first-order language in the signature with the constant 0, the functions S, +, and · , and the equality relation. Thus ...
PDF
... This article introduces and develops the theory of characteristic sequences. Fix V T a background theory and ϕ a formula. For each n < ω, set Pn (y1 , . . . yn ) := (∃x) i≤n ϕ(x; yi ). Then the characteristic sequence of ϕ is the countable sequence of hypergraphs hPn : n < ωi, each defined on the pa ...
... This article introduces and develops the theory of characteristic sequences. Fix V T a background theory and ϕ a formula. For each n < ω, set Pn (y1 , . . . yn ) := (∃x) i≤n ϕ(x; yi ). Then the characteristic sequence of ϕ is the countable sequence of hypergraphs hPn : n < ωi, each defined on the pa ...
Energy, Work, and Power
... 21. Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300-kg hot-dog cart rolls down a hill and then up another. When the cart reaches the top of the hill at point A, its speed is 8.00 m/s. a) How fast is the hot-dog cart going when it goes up the ...
... 21. Frank, a San Francisco hot dog vender, has fallen asleep on the job. When an earthquake strikes, his 300-kg hot-dog cart rolls down a hill and then up another. When the cart reaches the top of the hill at point A, its speed is 8.00 m/s. a) How fast is the hot-dog cart going when it goes up the ...
Automated Deduction
... The resolution calculus works on formulas in conjunctive normal form. Formulas in CNF will be notated by clause sets, defined below. Resolution is a refutational calculus, i.e. we start from a given clause set and try to show that it is unsatisfiable by showing that it implies a contradiction. This ...
... The resolution calculus works on formulas in conjunctive normal form. Formulas in CNF will be notated by clause sets, defined below. Resolution is a refutational calculus, i.e. we start from a given clause set and try to show that it is unsatisfiable by showing that it implies a contradiction. This ...
Chemistry - Manistique Area Schools
... The metal (sodium) tends to lose its one electron from the outer level. The nonmetal (chlorine) needs to gain one more to fill its outer level, and will accept the one electron that sodium is going to lose. ...
... The metal (sodium) tends to lose its one electron from the outer level. The nonmetal (chlorine) needs to gain one more to fill its outer level, and will accept the one electron that sodium is going to lose. ...
Superstring Theory and Empirical Testability - Philsci
... theories, and especially for fundamental physical theories, which guarantees certainty with regard to an adequate description of nature. Every criterion can, in particular in isolation, be criticized and dismantled, so that at the end our chances to do science in the traditional way look totally hop ...
... theories, and especially for fundamental physical theories, which guarantees certainty with regard to an adequate description of nature. Every criterion can, in particular in isolation, be criticized and dismantled, so that at the end our chances to do science in the traditional way look totally hop ...
A Friendly Introduction to Mathematical Logic
... you well and will help to introduce you to an area of mathematics that I have found fascinating and rewarding. Mathematical logic is absolutely central to mathematics, philosophy, and advanced computer science. The concepts that we discuss in this book—models and structures, completeness and incompl ...
... you well and will help to introduce you to an area of mathematics that I have found fascinating and rewarding. Mathematical logic is absolutely central to mathematics, philosophy, and advanced computer science. The concepts that we discuss in this book—models and structures, completeness and incompl ...
Oxford Master Course in Mathematical and Theoretical Physics
... areas and to those who have already firmly set their sights on one of the three subject areas (although they too are encouraged to explore across sub-field boundaries). Studies can be pursued with stronger emphasis on mathematical or on physical aspects. Appendix B gives examples of different pathwa ...
... areas and to those who have already firmly set their sights on one of the three subject areas (although they too are encouraged to explore across sub-field boundaries). Studies can be pursued with stronger emphasis on mathematical or on physical aspects. Appendix B gives examples of different pathwa ...
PDF
... α, β, γ, or δ, or by adding another element of S to the end of an open branch. The elements of S so added are called the premises of the tableau. We call a tableau complete, if every open branch is a Hintikka set for the universe of parameters and contains all the elements of S. Obviously every clos ...
... α, β, γ, or δ, or by adding another element of S to the end of an open branch. The elements of S so added are called the premises of the tableau. We call a tableau complete, if every open branch is a Hintikka set for the universe of parameters and contains all the elements of S. Obviously every clos ...
John L. Pollock
... The purpose of this book is to introduce the technical tools 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 ...
... The purpose of this book is to introduce the technical tools 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 ...