§24 Generators and Commutators
... {x1,x2, . . . ,xn} . In particular, if X = {x} consists of a single element, then x = {x} is the cyclic group generated by x, as we introduced in Definition 11.1. Definitions 11.1 and 24.1 are consistent, as will be proved in Lemma 24.2, below. Our notation ...
... {x1,x2, . . . ,xn} . In particular, if X = {x} consists of a single element, then x = {x} is the cyclic group generated by x, as we introduced in Definition 11.1. Definitions 11.1 and 24.1 are consistent, as will be proved in Lemma 24.2, below. Our notation ...
ANNALS OF PURE AND APPLIED LOGIC I W
... of the propositional calculus, in which programs are intermixed with propositions in a modal-like fashion. Formulas of PDL can express many input/output propertics of programs in a natural way. Moreover, validityisatisfiability in PDL is decidable in cxponential time, and the logic has a simple comp ...
... of the propositional calculus, in which programs are intermixed with propositions in a modal-like fashion. Formulas of PDL can express many input/output propertics of programs in a natural way. Moreover, validityisatisfiability in PDL is decidable in cxponential time, and the logic has a simple comp ...
![Rings of constants of the form k[f]](http://s1.studyres.com/store/data/021729650_1-3a6201c0eec615e02140355abcc4b661-300x300.png)
Rings of constants of the form k[f]
... Let k be a field of characteristic zero and let k[X] := k[x1 , . . . , xn ] be the polynomial ring in n variables over k. If d : k[X] → k[X] is a derivation of k[X], then we denote by k[X]d the ring of constants of d, that is, k[X]d = {w ∈ k[X]; d(w) = 0}. Rings of constants appear in various classi ...
... Let k be a field of characteristic zero and let k[X] := k[x1 , . . . , xn ] be the polynomial ring in n variables over k. If d : k[X] → k[X] is a derivation of k[X], then we denote by k[X]d the ring of constants of d, that is, k[X]d = {w ∈ k[X]; d(w) = 0}. Rings of constants appear in various classi ...
Default Reasoning in a Terminological Logic
... The field of TLs has lately been an active area of research, with the attention of researchers especially focusing on the investigation of their logical and computational properties. Nevertheless, few researchers have addressed the problem of extending these logics with the ability to perform defaul ...
... The field of TLs has lately been an active area of research, with the attention of researchers especially focusing on the investigation of their logical and computational properties. Nevertheless, few researchers have addressed the problem of extending these logics with the ability to perform defaul ...
Subset Types and Partial Functions
... deal with the case when X 'A Y contains free variables. Note that variables occurring free in a predicate P in a subset type A|P are considered part of the free variables of that type. The occurrence of X that is replaced cannot be beneath a λ-binding of any symbol x which occurs free in X 'A Y and ...
... deal with the case when X 'A Y contains free variables. Note that variables occurring free in a predicate P in a subset type A|P are considered part of the free variables of that type. The occurrence of X that is replaced cannot be beneath a λ-binding of any symbol x which occurs free in X 'A Y and ...
Document
... • Document your code!!!! – there is no way you can expect someone else to figure out what your program does with just your code ....since....in general it is provably impossible to do this! ...
... • Document your code!!!! – there is no way you can expect someone else to figure out what your program does with just your code ....since....in general it is provably impossible to do this! ...
