Finite Model Theory
... graphs, databases, computations etc. One of the underlying observatios behind the interest in finite model theory is that many of the problems of complexity theory and database theory can be formulated as problems of mathematical logic, provided that we limit ourselves to finite structures. While th ...
... graphs, databases, computations etc. One of the underlying observatios behind the interest in finite model theory is that many of the problems of complexity theory and database theory can be formulated as problems of mathematical logic, provided that we limit ourselves to finite structures. While th ...
On Quantum Simulators and Adiabatic Quantum Algorithms
... classical search algorithms and Hallgren’s quantum algorithm [6] for Pell’s equation1 which is exponentially faster than any known classical algorithm. Quantum mechanics, in so far as it is a complete natural theory, describes every physical computing device and, so, even classical computers. Theref ...
... classical search algorithms and Hallgren’s quantum algorithm [6] for Pell’s equation1 which is exponentially faster than any known classical algorithm. Quantum mechanics, in so far as it is a complete natural theory, describes every physical computing device and, so, even classical computers. Theref ...
CA208ex1 - DCU School of Computing
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
... Kate is a student. If Kate is a student, then Kate is broke. |= Kate is broke. Kate is a student. Kate is broke. |= Kate is a student and Kate is broke. Kate is a student and Kate is broke. |= Kate is a student. Kate is a student. |= Kate is a student. Kate is taller than John. John is taller than M ...
QUANTUM DYNAMICS OF A MASSLESS RELATIVISTIC
... provided only o'(0, r) = O, o'OT, r) = n. This invariance reflects the fact that these two functions define the same surface and should therefore be regarded as equivalent. There is a continuous infinity of functions which satisfy eq. (9) given the initial and final configurations. We must therefore ...
... provided only o'(0, r) = O, o'OT, r) = n. This invariance reflects the fact that these two functions define the same surface and should therefore be regarded as equivalent. There is a continuous infinity of functions which satisfy eq. (9) given the initial and final configurations. We must therefore ...
The Expressive Power of Modal Dependence Logic
... dependences, only propositional dependences can be expressed. This is due to the restriction that only proposition symbols are allowed in the dependence atoms of MDL. To overcome this defect Ebbing et al. [3] introduced the extended modal dependence logic, EMDL, which is obtained from MDL by extendi ...
... dependences, only propositional dependences can be expressed. This is due to the restriction that only proposition symbols are allowed in the dependence atoms of MDL. To overcome this defect Ebbing et al. [3] introduced the extended modal dependence logic, EMDL, which is obtained from MDL by extendi ...
x(t)
... Rather than 2 possible futures, there are many – but they can bee seen as a limit of many The probability to end up in xT is also given by the sum over all paths that ...
... Rather than 2 possible futures, there are many – but they can bee seen as a limit of many The probability to end up in xT is also given by the sum over all paths that ...
Constructive Mathematics, in Theory and Programming Practice
... the persuasive writings of Bishop, in which, as with Brouwer, the use of what became identified as intuitionistic logic was derived from an analysis of his perception of meaningful mathematical practice, we have been led, through our practice of Bishop-style mathematics, to a view that perhaps it is ...
... the persuasive writings of Bishop, in which, as with Brouwer, the use of what became identified as intuitionistic logic was derived from an analysis of his perception of meaningful mathematical practice, we have been led, through our practice of Bishop-style mathematics, to a view that perhaps it is ...
On Decidability of Intuitionistic Modal Logics
... C on the intuitionistic and modal accessibility relations, and conditions in C are of a certain form, then L is decidable.” The proof is a slight generalisation of the result in [6] and uses a translation into the two variable monadic guarded fragment of first order logic. Unfortunately, the decida ...
... C on the intuitionistic and modal accessibility relations, and conditions in C are of a certain form, then L is decidable.” The proof is a slight generalisation of the result in [6] and uses a translation into the two variable monadic guarded fragment of first order logic. Unfortunately, the decida ...
Predicate Languages - Computer Science, Stony Brook University
... Chapter 13: Predicate Languages Predicate Languages are also called First Order Languages. The same applies to the use of terms Propositional and Predicate Logic; they are often called zero Order and First Order Logics and we will use both terms equally. ...
... Chapter 13: Predicate Languages Predicate Languages are also called First Order Languages. The same applies to the use of terms Propositional and Predicate Logic; they are often called zero Order and First Order Logics and we will use both terms equally. ...
Verification Conditions Are Code - Electronics and Computer Science
... This does not invalidate the argument above, however, since C (Q;R) B can also be derived from C (Q;R) B and B ⇒ B. Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from t ...
... This does not invalidate the argument above, however, since C (Q;R) B can also be derived from C (Q;R) B and B ⇒ B. Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from t ...
ERCIM NEWS ntional Unconve
... may experience radically different proper times, have barely been addressed. Parallelism Weird physics isn’t the only property of the real world not addressed by the classical model. The real world is massively parallel, yet in the classical Turing model parallel computers are no more powerful than ...
... may experience radically different proper times, have barely been addressed. Parallelism Weird physics isn’t the only property of the real world not addressed by the classical model. The real world is massively parallel, yet in the classical Turing model parallel computers are no more powerful than ...
A Simple Tableau System for the Logic of Elsewhere
... extensions of this system are also defined, one related to the logical consequence relation and the other related to the addition of modal operators (without increasing the expressive power). An example of tableau proof is also presented. Different continuations of this work are proposed, one of the ...
... extensions of this system are also defined, one related to the logical consequence relation and the other related to the addition of modal operators (without increasing the expressive power). An example of tableau proof is also presented. Different continuations of this work are proposed, one of the ...
Physics 36300 - Particle Physics
... 37200. Space Physics and Astrophysics. 44300. Introduction to Quantum Field Theory I. 44400. Introduction to Quantum Field Theory II. 44500. Introduction to Quantum Field Theory III. Graduate Special Topics Courses 31700. Symplectic Methods of Classical Dynamics. Description TBA 38500. Advanced Mat ...
... 37200. Space Physics and Astrophysics. 44300. Introduction to Quantum Field Theory I. 44400. Introduction to Quantum Field Theory II. 44500. Introduction to Quantum Field Theory III. Graduate Special Topics Courses 31700. Symplectic Methods of Classical Dynamics. Description TBA 38500. Advanced Mat ...
A VIEW OF MATHEMATICS Alain CONNES Mathematics is the
... It is also vital to always keep moving. The risk otherwise is to confine oneself in a relatively small area of extreme technical specialization, thus shrinking one’s perception of the mathematical world and of its bewildering diversity. The really fundamental point in that respect is that while so m ...
... It is also vital to always keep moving. The risk otherwise is to confine oneself in a relatively small area of extreme technical specialization, thus shrinking one’s perception of the mathematical world and of its bewildering diversity. The really fundamental point in that respect is that while so m ...
Intuitionistic modal logic made explicit
... Justification logics are explicit modal logics in the sense that they unfold the -modality in families of so-called justification terms. Instead of formulas A, meaning that A is known, justification logics include formulas t : A, meaning that A is known for reason t. Artemov’s original semantics f ...
... Justification logics are explicit modal logics in the sense that they unfold the -modality in families of so-called justification terms. Instead of formulas A, meaning that A is known, justification logics include formulas t : A, meaning that A is known for reason t. Artemov’s original semantics f ...
Variations on a Montagovian Theme
... 2 + 2 = 5). The set L of logical truths, for example, is arithmetically sound, but it also contains very few arithmetical truths. A more informative theory is Robinson Arithmetic, also known as Q. Q can be axiomatised by five or six simple and uncontroversial statements about numbers, which can be f ...
... 2 + 2 = 5). The set L of logical truths, for example, is arithmetically sound, but it also contains very few arithmetical truths. A more informative theory is Robinson Arithmetic, also known as Q. Q can be axiomatised by five or six simple and uncontroversial statements about numbers, which can be f ...
Propositional Logic and Methods of Inference
... Note that p → q is equivalent to ~p v q SEEM 5750 ...
... Note that p → q is equivalent to ~p v q SEEM 5750 ...
Deciding Global Partial-Order Properties
... We begin with a model theory for the logic ISTL. Our models can be viewed in one of two ways: either as a partially ordered set of local states (states of individualprocesses), or as a branching structure (a Kripke model). The Kripke model represents all possible sequences of global states that may ...
... We begin with a model theory for the logic ISTL. Our models can be viewed in one of two ways: either as a partially ordered set of local states (states of individualprocesses), or as a branching structure (a Kripke model). The Kripke model represents all possible sequences of global states that may ...
Paper - Department of Computer Science and Information Systems
... set of equations axiomatising the variety of Boolean algebras with operators and additional equations corresponding the axioms of L. A closely related algorithmic problem for L is the admissibility problem for inference rules: given an inference rule ϕ1 , . . . , ϕn /ϕ, decide whether it is admissib ...
... set of equations axiomatising the variety of Boolean algebras with operators and additional equations corresponding the axioms of L. A closely related algorithmic problem for L is the admissibility problem for inference rules: given an inference rule ϕ1 , . . . , ϕn /ϕ, decide whether it is admissib ...