Multi-Agent Only
... I First-order modal logic for multi-agent only-knowing I Faithfully generalizes intuitions of Levesque’s logic I Semantics not based on Kripke structures or canonical models, and thus avoids some problems of ...
... I First-order modal logic for multi-agent only-knowing I Faithfully generalizes intuitions of Levesque’s logic I Semantics not based on Kripke structures or canonical models, and thus avoids some problems of ...
Introduction to Theoretical Computer Science, lesson 3
... Some more arguments If Charles has high blood pressure and breathes with difficulties or he has a fever then he is sick. Charles is not sick but he breathes with difficulties. What can be deduced from these facts? We have to distinguish between first and second reading because they are not equiva ...
... Some more arguments If Charles has high blood pressure and breathes with difficulties or he has a fever then he is sick. Charles is not sick but he breathes with difficulties. What can be deduced from these facts? We have to distinguish between first and second reading because they are not equiva ...
A Computing Procedure for Quantification Theory
... We i n t r o d u c e t h e following a b b r e v i a t i v e c o n v e n t i o n s : a s t a n d s for f~. f s t a n d s for f2. pq s t a n d s for p ( q ) if p is a f u n c t i o n s y m b o l a n d q is a t e r m . ~ ( p l , p2, "'" , pn) s t a n d s for "-~p(pl, " " , pn), where p is a p r e d i ...
... We i n t r o d u c e t h e following a b b r e v i a t i v e c o n v e n t i o n s : a s t a n d s for f~. f s t a n d s for f2. pq s t a n d s for p ( q ) if p is a f u n c t i o n s y m b o l a n d q is a t e r m . ~ ( p l , p2, "'" , pn) s t a n d s for "-~p(pl, " " , pn), where p is a p r e d i ...
DOC - John Woods
... Metatheory of CPL A big question is, “Why do we bother with proof theory?” After all, its principal concepts – axiom, theorem, deduction, proof – have no intuitive meaning there. What’s the point? Suppose we could show that for each of these uninterpreted properties of CPL’s proof theory theory is a ...
... Metatheory of CPL A big question is, “Why do we bother with proof theory?” After all, its principal concepts – axiom, theorem, deduction, proof – have no intuitive meaning there. What’s the point? Suppose we could show that for each of these uninterpreted properties of CPL’s proof theory theory is a ...
Quantum Field Theory
... high energies requires the use of special relativity. In some circumstances - think about elementary particle physics e.g. - one gets confronted with phenomena which simultaneously occur at high energies and small scales. The framework which unifies special relativity with quantum mechanics is relat ...
... high energies requires the use of special relativity. In some circumstances - think about elementary particle physics e.g. - one gets confronted with phenomena which simultaneously occur at high energies and small scales. The framework which unifies special relativity with quantum mechanics is relat ...
paper by David Pierce
... on (0, ∞), then we can show that N is closed under it, using integration by parts. Alternatively, we can just define this operation on N by requiring Γ(1) = 1 and Γ(x + 1) = Γ(x) · x, so that in general Γ(x) is what is usually denoted by (x − 1)!. The definition of N here is inductive; the proof that ...
... on (0, ∞), then we can show that N is closed under it, using integration by parts. Alternatively, we can just define this operation on N by requiring Γ(1) = 1 and Γ(x + 1) = Γ(x) · x, so that in general Γ(x) is what is usually denoted by (x − 1)!. The definition of N here is inductive; the proof that ...
predicate
... Reachability is Not Expressible • Theorem. There is no predicate-logic formula with u and v as its only free variables and R its only predicate such that holds in directed graphs iff there is a path from u to v. • Proof. By contradiction. Suppose there is such a formula. Let n be the formula e ...
... Reachability is Not Expressible • Theorem. There is no predicate-logic formula with u and v as its only free variables and R its only predicate such that holds in directed graphs iff there is a path from u to v. • Proof. By contradiction. Suppose there is such a formula. Let n be the formula e ...
Mathematical to Excel
... handle many situations; however, the ability to build a formula with the proper syntax is important. The key mathematical operators are ( ) Parenthesis pairs ^ Exponentiation * Multiply and / Divide + Addition and - Subtraction Excel caries out mathematical calculations in the hierarchy shown above. ...
... handle many situations; however, the ability to build a formula with the proper syntax is important. The key mathematical operators are ( ) Parenthesis pairs ^ Exponentiation * Multiply and / Divide + Addition and - Subtraction Excel caries out mathematical calculations in the hierarchy shown above. ...
Gödel`s Theorems
... 4.1.3. Substitution of numerals. In the sequel the elementary relation Sub representing substitution will not suffice. We shall need an elementary function s such that s(pC(z)q, k) = pC(k)q where k denotes the numeral k for the number k, defined by 0 := 0 and k + 1 := Sk (in any language with the fu ...
... 4.1.3. Substitution of numerals. In the sequel the elementary relation Sub representing substitution will not suffice. We shall need an elementary function s such that s(pC(z)q, k) = pC(k)q where k denotes the numeral k for the number k, defined by 0 := 0 and k + 1 := Sk (in any language with the fu ...
Gödel`s proof summary
... Meta-Mathematics. During the “foundational crisis”, meta-mathematics emerged as an important field of study. Meta-mathematics is when we “stand above” a mathematical system and make statements about it. Examples of mata-mathematical statements include: “Euclid proved 465 theorems in The Elements”; “ ...
... Meta-Mathematics. During the “foundational crisis”, meta-mathematics emerged as an important field of study. Meta-mathematics is when we “stand above” a mathematical system and make statements about it. Examples of mata-mathematical statements include: “Euclid proved 465 theorems in The Elements”; “ ...
Gregory Moore - Rutgers Physics
... Later, Moore & Witten explained in greater detail how these new invariants are related to the invariants of Donaldson. And Marino, Moore, and Peradze used the existence of N=2 superconformal fixed points to predict new results in the topology of four-manifolds. ...
... Later, Moore & Witten explained in greater detail how these new invariants are related to the invariants of Donaldson. And Marino, Moore, and Peradze used the existence of N=2 superconformal fixed points to predict new results in the topology of four-manifolds. ...
Newton`s Second Law
... • How much force is needed to accelerate a truck with a mass of 2,000 kilograms at a rate of 3 m/s/s? F = m×a = 2,000 kg × 3 m/s/s = 6,000 kg-m/s/s = 6,000 N • What is the mass of an object that requires 15 N to accelerate it at a rate of 1.5 m/s/s? m = F÷a = 15 N ÷ 1.5 m/s/s = 15 kg-m/s/s ÷1.5 m/s/ ...
... • How much force is needed to accelerate a truck with a mass of 2,000 kilograms at a rate of 3 m/s/s? F = m×a = 2,000 kg × 3 m/s/s = 6,000 kg-m/s/s = 6,000 N • What is the mass of an object that requires 15 N to accelerate it at a rate of 1.5 m/s/s? m = F÷a = 15 N ÷ 1.5 m/s/s = 15 kg-m/s/s ÷1.5 m/s/ ...
The statistical interpretation of quantum mechanics
... quantum numbers, are very large (that is to say, far to the right and to the lower part in the above array) and the energy changes relatively little from place to place, in fact practically continuously. Theoretical physics maintained itself on this concept for the next ten years. The problem was th ...
... quantum numbers, are very large (that is to say, far to the right and to the lower part in the above array) and the energy changes relatively little from place to place, in fact practically continuously. Theoretical physics maintained itself on this concept for the next ten years. The problem was th ...
Chapter 1
... clockwise manner.) Notice that even if our alphabet is such that orientation is not needed to identify symbols, it is still needed to identify expressions that are "left-right" juxtapositions of more than one symbol. b. How might the notion of shape be modified so that expressions of more than one s ...
... clockwise manner.) Notice that even if our alphabet is such that orientation is not needed to identify symbols, it is still needed to identify expressions that are "left-right" juxtapositions of more than one symbol. b. How might the notion of shape be modified so that expressions of more than one s ...
(p q r) (p q r) (p q r) (p q r) ( p q r)
... Complete elementary conjunction (CEC) of a given set S of elementary propositional symbols is an elementary conjunction in which each symbol (element of S) occurs just once: Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjun ...
... Complete elementary conjunction (CEC) of a given set S of elementary propositional symbols is an elementary conjunction in which each symbol (element of S) occurs just once: Ex.: p q Complete elementary disjunction (CED) of a given set S of elementary propositional symbols is an elementary disjun ...
REVERSE MATHEMATICS Contents 1. Introduction 1 2. Second
... Abstract. In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can b ...
... Abstract. In math we typically assume a set of axioms to prove a theorem. In reverse mathematics, the premise is reversed: we start with a theorem and try to determine the minimal axiomatic system required to prove the theorem (over a weak base system). This produces interesting results, as it can b ...
On a Symposium on the Foundations of Mathematics (1971) Paul
... This aim goes back to a critique of the method of founding analysis (by Dedekind, Cantor, Weierstraß), as expressed by some French mathematicians. This critique, while not going as far as that of Kronecker and later Brouwer, has in common with those sorts of views that it aims for a stricter arithm ...
... This aim goes back to a critique of the method of founding analysis (by Dedekind, Cantor, Weierstraß), as expressed by some French mathematicians. This critique, while not going as far as that of Kronecker and later Brouwer, has in common with those sorts of views that it aims for a stricter arithm ...
Slide 1
... Stoichiometry “In solving a problem of this sort, the grand thing is to be able to reason backward. This is a very useful accomplishment, and a very easy one, but people do not practice it much.” Sherlock Holmes, in Sir Arthur Conan Doyle’s A Study in Scarlet ...
... Stoichiometry “In solving a problem of this sort, the grand thing is to be able to reason backward. This is a very useful accomplishment, and a very easy one, but people do not practice it much.” Sherlock Holmes, in Sir Arthur Conan Doyle’s A Study in Scarlet ...
Relative normalization
... normalization as each axiomatic theory T requires a specific notion of reduction. Thus we use an extension of predicate logic called Deduction modulo [?]. In Deduction modulo, a theory is formed is formed with a set of axioms Γ and a congruence ≡ defined on formulæ. Then, the deduction rules take th ...
... normalization as each axiomatic theory T requires a specific notion of reduction. Thus we use an extension of predicate logic called Deduction modulo [?]. In Deduction modulo, a theory is formed is formed with a set of axioms Γ and a congruence ≡ defined on formulæ. Then, the deduction rules take th ...
AP Chemistry Ch. 3 Sections 3.5-3.6 Notes Percent Composition of
... • The mass percents of the elements in a compound can be determined by comparing the mass of each element present in 1 mole of the compound to the total mass of 1 mole of the compound. mass of element in 1 mole of compound • Mass percent of element = x 100% mass of 1 mole of compound • Example: • Fi ...
... • The mass percents of the elements in a compound can be determined by comparing the mass of each element present in 1 mole of the compound to the total mass of 1 mole of the compound. mass of element in 1 mole of compound • Mass percent of element = x 100% mass of 1 mole of compound • Example: • Fi ...
Sets with dependent elements: Elaborating on Castoriadis` notion of
... magma of my representations, I cannot strictly separate those that ‘refer to my family’ from those that do not. (In other words: among the representations which, at first sight, ‘do not refer to my family’ there is the first link of at least one coherent chain of representations leading to ‘my famil ...
... magma of my representations, I cannot strictly separate those that ‘refer to my family’ from those that do not. (In other words: among the representations which, at first sight, ‘do not refer to my family’ there is the first link of at least one coherent chain of representations leading to ‘my famil ...
A(x)
... A Model of the set of formulas {A1,…,An} is an interpretation I such that each of the formulas A1,...,An is true in I. Formula B logically follows from A1, …, An, denoted A1,…,An |= B, iff B is true in every model of {A1,…,An}. Thus for every interpretation I in which the formulas A1, …, An are true ...
... A Model of the set of formulas {A1,…,An} is an interpretation I such that each of the formulas A1,...,An is true in I. Formula B logically follows from A1, …, An, denoted A1,…,An |= B, iff B is true in every model of {A1,…,An}. Thus for every interpretation I in which the formulas A1, …, An are true ...
