Slide 1
... arbitrary surface, then it can always do so periodically. In other words, there must exist a finite area that can be tiled and then repeated infinitely often to cover any desired surface. But Wang’s conjecture is false. ...
... arbitrary surface, then it can always do so periodically. In other words, there must exist a finite area that can be tiled and then repeated infinitely often to cover any desired surface. But Wang’s conjecture is false. ...
Numerical Renormalization Group Calculations for Impurity
... bosonic degrees of freedom broadened the range of the parameter space to include the sub-ohmic case and, as a result, second order phase transitions were found for the bath exponent 0 < s < 1 (Bulla, Tong and Vojta 2003) as we discuss in Chapter 5. The bosonic single-impurity Anderson model (bsiAm) ...
... bosonic degrees of freedom broadened the range of the parameter space to include the sub-ohmic case and, as a result, second order phase transitions were found for the bath exponent 0 < s < 1 (Bulla, Tong and Vojta 2003) as we discuss in Chapter 5. The bosonic single-impurity Anderson model (bsiAm) ...
First-Order Logic with Dependent Types
... for the sort S. o is the type of formulas. The remainder of the signature encodes the usual grammar for FOL formulas. Higher-order abstract syntax is used, i.e., λ is used to bind the free variables in a formula, and quantifiers are operators taking a λ expression as an argument.2 Quantifiers and th ...
... for the sort S. o is the type of formulas. The remainder of the signature encodes the usual grammar for FOL formulas. Higher-order abstract syntax is used, i.e., λ is used to bind the free variables in a formula, and quantifiers are operators taking a λ expression as an argument.2 Quantifiers and th ...
Query Answering for OWL-DL with Rules
... some of the expressive power of OWL-DL: they are restricted to universal quantification and lack negation in their basic form. To overcome the limitations of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the ...
... some of the expressive power of OWL-DL: they are restricted to universal quantification and lack negation in their basic form. To overcome the limitations of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the ...
Linear Contextual Modal Type Theory
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
HKT Chapters 1 3
... • well-founded if every nonempty subset X ⊆ U has an R-minimal element; that is, an element b ∈ X such that for no a ∈ X is it the case that a R b. A binary relation R on U is called • a preorder or quasiorder if it is reflexive and transitive; • a partial order if it is reflexive, antisymmetric, and ...
... • well-founded if every nonempty subset X ⊆ U has an R-minimal element; that is, an element b ∈ X such that for no a ∈ X is it the case that a R b. A binary relation R on U is called • a preorder or quasiorder if it is reflexive and transitive; • a partial order if it is reflexive, antisymmetric, and ...
Chapter X: Computational Complexity of Propositional Fuzzy Logics
... There is a pattern in results presented in this chapter: for those decision problems whose complexity has been settled (the problems have been proved complete in some complexity class), the situation is analogous to the classical case: satisfiability is NP-complete, while tautologousness and consequ ...
... There is a pattern in results presented in this chapter: for those decision problems whose complexity has been settled (the problems have been proved complete in some complexity class), the situation is analogous to the classical case: satisfiability is NP-complete, while tautologousness and consequ ...
Sample pages 1 PDF
... densely ordered, i.e., between any two elements lies another one. A totally ordered subset K of a partially ordered set H is called a chain in H. Such a K is said to be bounded (to the above) if there is some b ∈ H with a b for all a ∈ K. Call c ∈ H maximal in H if no a ∈ H exists with a > c. An i ...
... densely ordered, i.e., between any two elements lies another one. A totally ordered subset K of a partially ordered set H is called a chain in H. Such a K is said to be bounded (to the above) if there is some b ∈ H with a b for all a ∈ K. Call c ∈ H maximal in H if no a ∈ H exists with a > c. An i ...
Everything is Knowable - Computer Science Intranet
... well-known postulate describes that if you revise a theory (set of formulas) with novel information described in a proposition p, then p should after that revision process form part of the theory, it should be believed! This postulate is called the success postulate. Initially, belief revision had n ...
... well-known postulate describes that if you revise a theory (set of formulas) with novel information described in a proposition p, then p should after that revision process form part of the theory, it should be believed! This postulate is called the success postulate. Initially, belief revision had n ...
Introducing Quantified Cuts in Logic with Equality
... in finite algebra. See also [11] for an approach to inductive theory formation. Our method of algorithmic cut-introduction, based on the inversion of Gentzen’s cut-elimination method, has been defined in [8] and [7]. The method in [8] works on a cut-free LK-proof ϕ of a prenex skolemized end-sequent S ...
... in finite algebra. See also [11] for an approach to inductive theory formation. Our method of algorithmic cut-introduction, based on the inversion of Gentzen’s cut-elimination method, has been defined in [8] and [7]. The method in [8] works on a cut-free LK-proof ϕ of a prenex skolemized end-sequent S ...
Document
... Arguments in Proposi:onal Logic • A argument in proposi:onal logic is a sequence of proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is ...
... Arguments in Proposi:onal Logic • A argument in proposi:onal logic is a sequence of proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is ...
CHAPTER 1 The main subject of Mathematical Logic is
... for their average. It is possible to “extract” this algorithm from the formalized proof. This extract will be a term of the underlying logical language. However, for efficiency reasons one may later translate it into a functional programming language (like Scheme or Haskell). An obvious advantage of ...
... for their average. It is possible to “extract” this algorithm from the formalized proof. This extract will be a term of the underlying logical language. However, for efficiency reasons one may later translate it into a functional programming language (like Scheme or Haskell). An obvious advantage of ...
A Simple and Practical Valuation Tree Calculus for First
... Keywords: formal systems, proof theory. ...
... Keywords: formal systems, proof theory. ...
Recently an undergraduate engineering student asked me if
... doctoral degree. Another five years passed before I felt comfortable with what physics and mathematics mean in their most general formulations. The best suggestion I ever received from a professor was to get into the habit of collecting toy models of core ideas. Looking back at my experience, I can ...
... doctoral degree. Another five years passed before I felt comfortable with what physics and mathematics mean in their most general formulations. The best suggestion I ever received from a professor was to get into the habit of collecting toy models of core ideas. Looking back at my experience, I can ...
THE DEMYSTIFICATION OF EMERGENT
... As one lowers the energy scale to the point where the interaction between distinct protons and neutrons becomes important, new internal degrees of freedom appear that are not contained in the higher energy theory. One might well view the properties of the low-energy regime as being emergent. Althoug ...
... As one lowers the energy scale to the point where the interaction between distinct protons and neutrons becomes important, new internal degrees of freedom appear that are not contained in the higher energy theory. One might well view the properties of the low-energy regime as being emergent. Althoug ...
Digital Logic and the Control Unit
... chapter with a discussion of Boolean algebra, which has become the basis for all digital logic. Boolean algebra, also called “Boolean logic”, was invented by the English mathematician and philosopher George Boole. Boolean algebra is based on Boole’s 1854 book with the rather long title “An Investiga ...
... chapter with a discussion of Boolean algebra, which has become the basis for all digital logic. Boolean algebra, also called “Boolean logic”, was invented by the English mathematician and philosopher George Boole. Boolean algebra is based on Boole’s 1854 book with the rather long title “An Investiga ...
Advanced Topics in Theoretical Computer Science
... Decidability and Undecidability results Theorem. It is undecidable whether a first order logic formula is valid. Proof. Suppose there is an algorithm P that, given a first order logic and a formula in that logic, decides whether that formula is valid. We use P to give a decision algorithm for the l ...
... Decidability and Undecidability results Theorem. It is undecidable whether a first order logic formula is valid. Proof. Suppose there is an algorithm P that, given a first order logic and a formula in that logic, decides whether that formula is valid. We use P to give a decision algorithm for the l ...
Problem_Set_01
... 2. Aristotle’s Proof that the Square Root of Two is Irrational. a. Prove the lemma, used by Aristotle in his proof, which says that if n2 is even, so is n. (Hint: Remember that a b is equivalent to b a). b. Prove that the square root of 3 is irrational using Aristotle’s techniques. Make sure t ...
... 2. Aristotle’s Proof that the Square Root of Two is Irrational. a. Prove the lemma, used by Aristotle in his proof, which says that if n2 is even, so is n. (Hint: Remember that a b is equivalent to b a). b. Prove that the square root of 3 is irrational using Aristotle’s techniques. Make sure t ...