Boolean

A CONSTRUCT is an entity that has a scope. The data structure of a construct represents a three-dimensional geometrical shape. Certain domains of this shape may have material properties associated with them. A construct is not an elementary solid model but defines a function which -when evaluated- will produce a solid. The function operators are BOOLEAN, the operands are of type BOOL OPERAND. The elementary operands which are called PRIMITIVE entities exist in the scope of the CONSTRUCT only. However, POLYHEDRON models and B REP entities may exist in the construct scope and may be used as operands to boolean operations (if the CAD system provides this capability). The attribute result is an instance of the BOOLEAN which represents the root of the boolean tree or simply of a PRIMITIVE, B REP, POLYHEDRON, or another CONSTRUCT. 

ENTITY BOOLEAN = STRUCTURE operator first operand second operand END  

REFERENCE(BOOL OPERAND) REFERENCE(BOOL OPERAND)  

BOOL OPERAND is a class of entities which can occur as an operand to a BOOLEAN operation using regularized boolean operators (see e.g. A.A.G.Requicha and H.B.Voelcker, Solid Modeling, in IEEE Computer Graphics and Applications, Vol.2, No.2, Mar. 1982, pp.9-24) 

ATTRIBUTE BOOI OPERATOR = ENUM( DIFFERENCE, UNION, INTERSECTION ) bool operator = DIFFERENCE UNION INTERSECTION 

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Knowledge of Boolean and other advanced search features 3 Time... 

Many basic mathematical functions already exists(FFT, loops, booleans,. ), which simplifies the work of the programmer. 

Formula, Boolean, Matrices, Connection Table, Mashcode, etc. 

The adjacency matrix of a molecule con.si.sting of n atom.s i.s a square (n / n) matrix. with the entric.s giving all the connectivities of the atoms. The intersection of a row and a column obtains a value of 1 if the corresponding atoms are connected. If there is no bond between the atoms being considered, the position in the matrix obtains the value 0. Thus, this matrix representation is a Boolean matrix with bits (0 or I) (Figure 2-13). 

The initial step is to identify which database, from a few thousands worldwide (about 10 000 in 2002), provides the requested information. The next step is to determine which subsection of the topic is of interest, and to identify typical search terms or keywords (synonyms, homonyms, different languages, or abbreviations) (Table 5-1). During the search in a database, this strategy is then executed (money is charged for spending time on some chemical databases). The resulting hits may be further refined by combining keywords or database fields, respectively, with Boolean operators (Table 5-2). The final results should be saved in electronic or printed form. 

Databo e-s and Data Sources in Chemi-stry 231 Table 5-2. Basic search tools of Boolean operators and truncation. 

The Boolean search operators are used to specify Logical relationships among the terms being searched. 

The Web-based graphical user interface permits a choice from numerous criteria and the performance of rapid searches. This service, based on the chemistry information toolkit CACTVS, provides complex Boolean searches. Flexible substructure searches have also been implemented. Users can conduct 3D pharmacophore queries in up to 25 conformations pre-calculated for each compound. Numerous output formats as well as 2D and 3D visuaHzation options are supplied. It is possible to export search results in various forms and with choices for data contents in the exported files, for structure sets ranging in size from a single compound to the entire database. Additional information and down-loadable files (in various formats) can be obtained from this service. 

Structural keys describe the chemical composition and structural motifs of molecules represented as a Boolean array. If a certain structural feature is present in a molecule or a substructure, a particular bit is set to 1 (true), otherwise to 0 (false). A bit in this array may encode a particular functional group (such as a carboxylic acid or an amidelinkage), a structural element (e.g., a substituted cyclohexane), or at least n occurrences of a particular element (e.g., a carbon atom). Alternatively, the structural key can be defined as an array of integers where the elements of this array contain the frequency of a specific feature in the molecule. 

Conventional computers initially were not conceived to handle vague data. Human reasoning, however, uses vague information and uncertainty to come to a decision. In the mid-1960 this discrepancy led to the conception of fuzzy theory [14]. In fuzzy logic the strict scheme of Boolean logic, which has only two statements true and false), is extended to handle information about partial truth, i.e., truth values between "absolutely true" and absolutely false". It thus gives a mathematical representation of uncertainty and vagueness and provides a tool to treat them. 

Many expert systems also apply fnt zy logic (see Section 9.6) instead of strict Boolean logic and arc thus able to cope with rules which arc imprecise or incomplete. 

Fuzzy logic extends the Boolean logic so as to handle information about truth values which are between absolutely true and "absolutely false . 

Answers from aH of these searches contain CAS Registry Numbers. Answer sets may be combined, using the Boolean operators AND, OR, or NOT, with other answer sets or with text terms, such as names or molecular formulas. Any answer set also may be used to define subsets of the file for subsequent stmcture searching. Answer sets of up to 10,000 Registry Numbers from any type of search in this file may also be used as search terms in other files, such as the CA or CAOLD files (53). 

Coordinate Indexing and Boolean Logic. Three methods of indexing have been prominent in the chemical Hterature in recent times. The first, articulated indexing, has been used in printed Chemicaly hstracts subject indexes from their earliest days until well into the 1990s. A number of important concepts are identified as permissible index entries, including specific compounds, material types, reactions, and processes. One or more modifying statements foUow each basic index entry. Thus, eg. 

In the earliest days of on-line databases, all three indexing types coUapsed into the third. Using older manual tools, it was difficult to coordinate more than two or three concepts, but the computer made that easier. Each concept in a search can be represented by a string of synonyms or alternatives, and searching can be done for two such parameters or more. Thus, Boolean logic expressions can easily be constmcted as follows ... 

Full-Text Patent Databases. The LEXPAT database on the LEXIS— NEXIS system, the first commercially available full-text patent file, receives its greatest use from patent attorneys and has been relatively unused by other patent information speciaUsts. This may be attributed to search software that is quite different from the type familiar to information speciaUsts, no matter what their preferred host system. This situation has changed with dialog s release of the PATEULL files followed by STN s USPATEULL, both searchable by familiar Boolean techniques and featuring greater... 

The multiloop controller contains a variety of func tion blocks (for example, PID, totalizer, lead/lag compensator, ratio control, alarm, sequencer, and Boolean) that can be soft-wired together to form complex control strategies. The multiloop controller, as part of a DCS, communicates with other controllers and man/machine interface (MMI) devices also on the DCS network. 

Programmable Logic Controllers The programmable logic controller (PLC) originated as a solid-state replacement for the hardwired relay control panel and was first used in the automotive indus-tiy for discrete manufacturing control. Today, PLCs are used to implement Boolean logic functions, timers, counters, and some math functions and PID control. PLCs are often used with on/off process control valves. 

The logical structure of a fault tree can be described in terms of boolean algebraic equations. Some specific prerequisites to the application of this methodology are as follows. 

Identification and quantitative estimation of common-cause failures are general problems in fault tree analysis. Boolean approaches are generally better smted to mathematically handle common-cause failures. 

Union The union of two fuzzy sets A and B eorresponds to the Boolean OR funetion and is given by... 

From equation (10.5) the Boolean OR function becomes the fuzzy max operation, and from equation (10.6) the Boolean AND function becomes the fuzzy min operation. Hence equation (10.22) can be written as... 

Table 2.1-1 compares the ordinary algebra of continuous variables with the Boolean algebra of 1 s and Os. This table uses the symbols and -h for the operations of intersection (AND) and union (OR) which mathematicians represent by n and u respectively. The symbols and -f which are the symbols of multiplication and addition, are used because of the similarity of their use to AND and OR in logic. 

In the table, the rules of commutation, association and distribution are the same for both algebras. Idempotency, unique to Boolean algebra, relates to redundancy. Having "A and A is the same as only having A A or A is superfluous and equals A. Complementation is introduced in the next rule. The universe is represented by 1 . Completeness includes every thing in this world and not in this world, hence A +A = 1 where not A is A 1 -A which is the meaning of complementation. With this understanding, it is impossible to be both A and not A. Similarly A or not A is complete (the universe). Under unity, A is included in the universe (1) so A-f 1 = 1 For this... 

Systems may be modeled using Boolean algebra with two-.state representation of component operability. Systems are not usually modeled as equations is not usually done because of preference by engineers for the more schematic methods that are presented in the next chapter. 

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