Preference Planning for Markov Decision Processes
... We implemented the P4Solver algorithm in Scala and delegated to Z3 (de Moura and Bjørner 2008) the evaluation of the generated quadratic programming problem. We represent each state of the MDP by the atomic propositions it is labelled with; for instance, the state of the MDP depicted in Figure 1 is ...
... We implemented the P4Solver algorithm in Scala and delegated to Z3 (de Moura and Bjørner 2008) the evaluation of the generated quadratic programming problem. We represent each state of the MDP by the atomic propositions it is labelled with; for instance, the state of the MDP depicted in Figure 1 is ...
2.50 g O 2 1 mol O 2 31.99 g O 2
... 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.” ...
... 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.” ...
What is quantum chaos?
... 1. Quantum classical transition. 2. Nano-Meso physics. Quantum engineering. 3. Systems with interactions for which the exact Schrödinger equation cannot be solved. ...
... 1. Quantum classical transition. 2. Nano-Meso physics. Quantum engineering. 3. Systems with interactions for which the exact Schrödinger equation cannot be solved. ...
Predicate Calculus - National Taiwan University
... Mary’s father likes music One possible way: ∃x(f(x, Mary)∧Likes(x,Music)) which means: Mary has at least one father and he ...
... Mary’s father likes music One possible way: ∃x(f(x, Mary)∧Likes(x,Music)) which means: Mary has at least one father and he ...
Formal Scattering Theory for Energy
... theory has a long history in atomic, nuclear and particle physics. The best known examples are the 'optical potentials' which arise when many channel problems are reduced to equivalent one channel problems (see e.g. Goldberger and Watson 1964 or Mott and Massey 1965). Other examples are the nucleon- ...
... theory has a long history in atomic, nuclear and particle physics. The best known examples are the 'optical potentials' which arise when many channel problems are reduced to equivalent one channel problems (see e.g. Goldberger and Watson 1964 or Mott and Massey 1965). Other examples are the nucleon- ...
“Sometimes” and “Not Never” Revisited
... there exists a total, binary relation R on S such that X consists precisely of the infinite sequences (so, sI, s2, . . .) of states from X for which (Si, si+l ) E R. R-generability corresponds to the common approach (cf. [2, 7, 9, 13, 211) of describing a concurrent program via a transition relation ...
... there exists a total, binary relation R on S such that X consists precisely of the infinite sequences (so, sI, s2, . . .) of states from X for which (Si, si+l ) E R. R-generability corresponds to the common approach (cf. [2, 7, 9, 13, 211) of describing a concurrent program via a transition relation ...
Formalizing Basic First Order Model Theory
... mainly in Mizar [14, 11], it is perhaps hardly noteworthy to formalize yet another fragment. However, we believe that the present work does at least raise a few interesting general points. – Formalization of syntax constructions involving bound variables has inspired a slew of research; see e.g. Cha ...
... mainly in Mizar [14, 11], it is perhaps hardly noteworthy to formalize yet another fragment. However, we believe that the present work does at least raise a few interesting general points. – Formalization of syntax constructions involving bound variables has inspired a slew of research; see e.g. Cha ...
x - unist
... y ( , x) y ( x) ( x) where η is some function of x that has a continuous derivatives (to the desired level) and that vanishes at x1 and x2 (or any other conditions necessary to satisfy the boundary conditions). Then, our original y becomes y(0,x). J is in principle a functional of y. However ...
... y ( , x) y ( x) ( x) where η is some function of x that has a continuous derivatives (to the desired level) and that vanishes at x1 and x2 (or any other conditions necessary to satisfy the boundary conditions). Then, our original y becomes y(0,x). J is in principle a functional of y. However ...
University of Groningen M-theory and gauged supergravities Roest
... expect cancellation of certain non-renormalisable infinities. A more radical idea than supergravity seems to be required for quantum gravity. At the moment, the most promising candidate is string theory. It first surfaced in the 1960s in the context of certain scattering amplitudes of hadrons [10] ( ...
... expect cancellation of certain non-renormalisable infinities. A more radical idea than supergravity seems to be required for quantum gravity. At the moment, the most promising candidate is string theory. It first surfaced in the 1960s in the context of certain scattering amplitudes of hadrons [10] ( ...
remarks on synthetic tableaux for classical propositional calculus
... In contradistinction to Beth-like semantic tableaux, which are founded on the reductio ad absurdum procedure, STM is based on a direct reasoning. STM is constructive in the sense that a proof of a formula A is built up as a set of inferences of A from, defined in a suitable way, consistent sets of pr ...
... In contradistinction to Beth-like semantic tableaux, which are founded on the reductio ad absurdum procedure, STM is based on a direct reasoning. STM is constructive in the sense that a proof of a formula A is built up as a set of inferences of A from, defined in a suitable way, consistent sets of pr ...
Lesson 12
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
Fulltext PDF
... negative or zero), these generalized charges are matrices which do not commute with each other and hence can be called `nonabelian charges'1. Electrodynamics which is based on the abelian charge is called abelian gauge theory and the generalization based on nonabelian charges is called nonabelian ga ...
... negative or zero), these generalized charges are matrices which do not commute with each other and hence can be called `nonabelian charges'1. Electrodynamics which is based on the abelian charge is called abelian gauge theory and the generalization based on nonabelian charges is called nonabelian ga ...
Doctoral Programmes in Physics at IMSc
... examples: free particle, one-dimensional potential well, potential barrier, harmonic oscillator, etc., Hilbert space formulation of Quantum Mechanics: states, observables, measurement, evolution, collapse of wave function, uncertainty relation and its interpretation, Discrete and continuous spectra, ...
... examples: free particle, one-dimensional potential well, potential barrier, harmonic oscillator, etc., Hilbert space formulation of Quantum Mechanics: states, observables, measurement, evolution, collapse of wave function, uncertainty relation and its interpretation, Discrete and continuous spectra, ...
University Chemistry The Modern Atomic Theory Structure of Atoms
... The Modern Atomic Theory Modern Atomic theory has four assumptions: 1. Atoms make up all matter. 2. The atoms of one element are different from the atoms of another element. 3. Atoms combine in definite ratios to make compounds. 4. Combinations of atoms in compounds can change only when a chemical r ...
... The Modern Atomic Theory Modern Atomic theory has four assumptions: 1. Atoms make up all matter. 2. The atoms of one element are different from the atoms of another element. 3. Atoms combine in definite ratios to make compounds. 4. Combinations of atoms in compounds can change only when a chemical r ...
(A B) |– A
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
(A B) |– A
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
... Notes: 1. A, B are not formulas, but meta-symbols denoting any formula. Each axiom schema denotes an infinite class of formulas of a given form. If axioms were specified by concrete formulas, like 1. p (q p) 2. (p (q r)) ((p q) (p r)) 3. (q p) (p q) we would have to extend th ...
1 Formal Languages
... Oftentimes – for example, in many of the numbered sentences above – we are not using a sentence but only mentioning it. This illustrates another very important linguistic convention. A linguistic expression can be mentioned by setting it off typographically. One off-set method is to set it on its ow ...
... Oftentimes – for example, in many of the numbered sentences above – we are not using a sentence but only mentioning it. This illustrates another very important linguistic convention. A linguistic expression can be mentioned by setting it off typographically. One off-set method is to set it on its ow ...
The initial question: “What is the meaning of a first
... that synonymy relation restricted to the set of variables is not the universal relation. (5) A structural semantic feature of a variable is ambiguity and denotational behaviour. ...
... that synonymy relation restricted to the set of variables is not the universal relation. (5) A structural semantic feature of a variable is ambiguity and denotational behaviour. ...
Decision Procedures for Flat Array Properties
... We examine Flat Array Properties in two different settings. In one case, we consider Flat Array Properties over the theory of arrays generated by adding free function symbols to a given theory T modeling both indexes and elements of the arrays. In the other one, we take into account Flat Array Prope ...
... We examine Flat Array Properties in two different settings. In one case, we consider Flat Array Properties over the theory of arrays generated by adding free function symbols to a given theory T modeling both indexes and elements of the arrays. In the other one, we take into account Flat Array Prope ...
Peano and Heyting Arithmetic
... π(σ _ hni) for actual sequences σ and natural numbers n. But this isn’t enough to give the last two clauses, because HA can’t actually prove that the numerals n are the only numbers. So the last two clauses say that HA can actually prove that φ_ represents a well-defined function. (For instance, the ...
... π(σ _ hni) for actual sequences σ and natural numbers n. But this isn’t enough to give the last two clauses, because HA can’t actually prove that the numerals n are the only numbers. So the last two clauses say that HA can actually prove that φ_ represents a well-defined function. (For instance, the ...
Progress In N=2 Field Theory - Rutgers Physics
... Extended QFT and N-Categories The inclusion of these extended objects enriches the notion of quantum field theory. Even in the case of topological field theory, the usual formulation of Atiyah and Segal is enhanced to ``extended TQFT’s’’ leading to beautiful relations to N-categories and the ``cobo ...
... Extended QFT and N-Categories The inclusion of these extended objects enriches the notion of quantum field theory. Even in the case of topological field theory, the usual formulation of Atiyah and Segal is enhanced to ``extended TQFT’s’’ leading to beautiful relations to N-categories and the ``cobo ...
3x9: 9 E 9}, V{ A 8: 9 ES)
... above, to contain just one element. Thus, by (i), |6„| < k, contradicting the largeness of a. Now, using Claim 8, one constructs precisely as in the proof of Theorem 1, a tree 7;, s E<"2 s.t. for all s: (a) Ts is finite, a E Ts and /\TS is large; (b) there is \p E ^ s.t. \L E TsA<0y and -jt// E rjA< ...
... above, to contain just one element. Thus, by (i), |6„| < k, contradicting the largeness of a. Now, using Claim 8, one constructs precisely as in the proof of Theorem 1, a tree 7;, s E<"2 s.t. for all s: (a) Ts is finite, a E Ts and /\TS is large; (b) there is \p E ^ s.t. \L E TsA<0y and -jt// E rjA< ...
Lecture 14 Notes
... first-order truth set is exactly the set of all formulas that are true under a fixed first-order valuation. The definition of first-order valuations can be extended to sentences with parameters as follows. Let ϕ be a mapping from the set of parameters to U. For a formula A define Aϕ to be the result ...
... first-order truth set is exactly the set of all formulas that are true under a fixed first-order valuation. The definition of first-order valuations can be extended to sentences with parameters as follows. Let ϕ be a mapping from the set of parameters to U. For a formula A define Aϕ to be the result ...