Pub Date : 2017-12-31DOI: 10.7591/9781501719066-007
A. Reyes, Lise Geetoor, T. Pressburger
identity of ΣA and ABS, program fragments are returned in the language ofΣC. A decision procedure replaces deductive inference on the axioms in DT. As in DRAT, the library is organized hierarchically; a new portion of the library is shown in Figure 1. Each node in the hierarchy is a 6-tuple where the first four elements are the index,DP is a decision procedure schema (implemented as a common lisp object class), and I is a procedure for instantiating a decision procedure schema given an instantiation of the 4-tuple index. When the theory resolution interface gives an instantiated decision procedure a set of literals in the language of ΣA and ABS,the decision procedure returns terms in the language of ΣC as bindings for existential variables in the literals (universal variables when considered as an unsatisfiability problem). The decision procedure can also return a set of residual literals, if it is unable to completely resolve the literals given as input. More formally, given a set φ of literals in the language of ΣA and ABS, the decision procedure returns a set of literals φ ’ and set of terms t in the language of ΣC, such that ( outsare variables, DTI is the instantiated theory for the decision procedure): As an example, consider the decision procedures indexed under the Graph taxonomy in Figure 1. These decision procedures generate terms representing paths in a graph. The specification language ( ΣA) sort ‘nodes’ consist of the node labels of the graph, and the concrete language ( ΣC) sort ‘edges’ consist of the edge labels of the graph. The properties of the graph determine which decision procedure in the taxonomy is used. A decision procedure is applicable if an instantiation of its theory (i.e., DTI) is implied by the domain theory defining a graph; the decision procedure with the most specific such theory is best. Instantiated decision procedures from the Graph taxonomy take as input conjunctions of literals and build internal graph data structures representing those conjunctions. These decision procedures decide satisfiability of the conjunctions (with respect to the instantiated theory for the decision procedure) by manipulating the graphs. They also determine when variables in the conjunction are connected in the graph to constants (program input variables) and construct ground terms for those variables by traversing the graph. Instantiated decision procedures can be composed horizontally or vertically (where the concrete language for one decision procedure is the same as the abstract language for the following decision procedure). When decision procedures are combined, they communicate by passing variable bindings back and forth [7]. In addition, decision procedures can be nested —one decision procedure can take another as a parameter in order to solve subproblems. Each decision procedure in the Graph taxonomy is parameterized by a path algebra; this parameter is instantiated by a decision procedure in the hierarchy
{"title":"7 Conclusion","authors":"A. Reyes, Lise Geetoor, T. Pressburger","doi":"10.7591/9781501719066-007","DOIUrl":"https://doi.org/10.7591/9781501719066-007","url":null,"abstract":"identity of ΣA and ABS, program fragments are returned in the language ofΣC. A decision procedure replaces deductive inference on the axioms in DT. As in DRAT, the library is organized hierarchically; a new portion of the library is shown in Figure 1. Each node in the hierarchy is a 6-tuple <DT,ΣA,ΣC,ABS,I,DP>where the first four elements are the index,DP is a decision procedure schema (implemented as a common lisp object class), and I is a procedure for instantiating a decision procedure schema given an instantiation of the 4-tuple index. When the theory resolution interface gives an instantiated decision procedure a set of literals in the language of ΣA and ABS,the decision procedure returns terms in the language of ΣC as bindings for existential variables in the literals (universal variables when considered as an unsatisfiability problem). The decision procedure can also return a set of residual literals, if it is unable to completely resolve the literals given as input. More formally, given a set φ of literals in the language of ΣA and ABS, the decision procedure returns a set of literals φ ’ and set of terms t in the language of ΣC, such that ( outsare variables, DTI is the instantiated theory for the decision procedure): As an example, consider the decision procedures indexed under the Graph taxonomy in Figure 1. These decision procedures generate terms representing paths in a graph. The specification language ( ΣA) sort ‘nodes’ consist of the node labels of the graph, and the concrete language ( ΣC) sort ‘edges’ consist of the edge labels of the graph. The properties of the graph determine which decision procedure in the taxonomy is used. A decision procedure is applicable if an instantiation of its theory (i.e., DTI) is implied by the domain theory defining a graph; the decision procedure with the most specific such theory is best. Instantiated decision procedures from the Graph taxonomy take as input conjunctions of literals and build internal graph data structures representing those conjunctions. These decision procedures decide satisfiability of the conjunctions (with respect to the instantiated theory for the decision procedure) by manipulating the graphs. They also determine when variables in the conjunction are connected in the graph to constants (program input variables) and construct ground terms for those variables by traversing the graph. Instantiated decision procedures can be composed horizontally or vertically (where the concrete language for one decision procedure is the same as the abstract language for the following decision procedure). When decision procedures are combined, they communicate by passing variable bindings back and forth [7]. In addition, decision procedures can be nested —one decision procedure can take another as a parameter in order to solve subproblems. Each decision procedure in the Graph taxonomy is parameterized by a path algebra; this parameter is instantiated by a decision procedure in the hierarchy ","PeriodicalId":127029,"journal":{"name":"Buddhist Revitalization and Chinese Religions in Malaysia","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121764212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-07-11DOI: 10.1163/9789004255678_010
U. Theobald
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