SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is predicate dat...SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is predicate data flow diagram (PDFD). In order to eliminate the ambiguity of predicate data flow diagrams and their associated textual specifications, a formalization of the syntax and semantics of predicate data flow diagrams is necessary. In this paper we use Z notation to define an abstract syntax and the related structural constraints for the PDFD notation, and provide it with an axiomatic semantics based on the concept of data availability and functionality of predicate operation. Finally, an example is given to establish functionality consistent decomposition on hierarchical PDFD (HPDFD).展开更多
Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the ...Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.展开更多
In the current biomedical data movement, numerous efforts have been made to convert and normalize a large number of traditional structured and unstructured data (e.g., EHRs, reports) to semi-structured data (e.g., RDF...In the current biomedical data movement, numerous efforts have been made to convert and normalize a large number of traditional structured and unstructured data (e.g., EHRs, reports) to semi-structured data (e.g., RDF, OWL). With the increasing number of semi-structured data coming into the biomedical community, data integration and knowledge discovery from heterogeneous domains become important research problem. In the application level, detection of related concepts among medical ontologies is an important goal of life science research. It is more crucial to figure out how different concepts are related within a single ontology or across multiple ontologies by analysing predicates in different knowledge bases. However, the world today is one of information explosion, and it is extremely difficult for biomedical researchers to find existing or potential predicates to perform linking among cross domain concepts without any support from schema pattern analysis. Therefore, there is a need for a mechanism to do predicate oriented pattern analysis to partition heterogeneous ontologies into closer small topics and do query generation to discover cross domain knowledge from each topic. In this paper, we present such a model that predicates oriented pattern analysis based on their close relationship and generates a similarity matrix. Based on this similarity matrix, we apply an innovated unsupervised learning algorithm to partition large data sets into smaller and closer topics and generate meaningful queries to fully discover knowledge over a set of interlinked data sources. We have implemented a prototype system named BmQGen and evaluate the proposed model with colorectal surgical cohort from the Mayo Clinic.展开更多
Respectively belonging to different language families,English and Chinese naturally have many differences in morphology and syntax.This paper intends to give a contrastive analysis of subject and predicate in English ...Respectively belonging to different language families,English and Chinese naturally have many differences in morphology and syntax.This paper intends to give a contrastive analysis of subject and predicate in English and Chinese,focusing on differences of subject and predicate usages in the two languages,and the problems they cause for Chinese students in English learning and translation.展开更多
This paper described an approach to make inferences on Chinese information using first order predicate logic, which could be used in the semantic query of Chinese. The predicates of the method were derived from the na...This paper described an approach to make inferences on Chinese information using first order predicate logic, which could be used in the semantic query of Chinese. The predicates of the method were derived from the natural language using rule based LFT, the axiom set was generated by extracting lexicon knowledge from HowNet, and the first order predicate inferences were made through symbol connection of center words. After all these were done, the evaluation and possible improvements of the method were provided. The experiment result shows a higher precision rate than that traditional methods can reach.展开更多
A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a ...A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a Petri net with predicated transition. All components of the net are expressed by annotation which is defined on rational set Q. The analysis method for the plant is interval temporal logic represented by Petri nets. This paper combines the above two methods to synthesize the hybrid system, gives a simple and clear expression of the expected action of the studied plant.展开更多
Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive process...Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive processing of noun predicate sentences.Therefore,under the framework of cognitive grammar,this paper tries to analyze the semantic connection and cognitive process in noun predicate sentences from the semantic perspective and the method of example theory,and discusses the motivation of the formation of this construction,so as to provide references for in-depth analysis of the cognitive laws behind noun predicate sentences.展开更多
This paper explores a tree kernel based method for semantic role labeling (SRL) of Chinese nominal predicates via a convolution tree kernel. In particular, a new parse tree representation structure, called dependenc...This paper explores a tree kernel based method for semantic role labeling (SRL) of Chinese nominal predicates via a convolution tree kernel. In particular, a new parse tree representation structure, called dependency-driven constituent parse tree (D-CPT), is proposed to combine the advantages of both constituent and dependence parse trees. This is achieved by directly representing various kinds of dependency relations in a CPT-style structure, which employs dependency relation types instead of phrase labels in CPT (Constituent Parse Tree). In this way, D-CPT not only keeps the dependency relationship information in the dependency parse tree (DPT) structure but also retains the basic hierarchical structure of CPT style. Moreover, several schemes are designed to extract various kinds of necessary information, such as the shortest path between the nominal predicate and the argument candidate, the support verb of the nominal predicate and the head argument modified by the argument candidate, from D-CPT. This largely reduces the noisy information inherent in D-CPT. Finally, a convolution tree kernel is employed to compute the similarity between two parse trees. Besides, we also implement a feature-based method based on D-CPT. Evaluation on Chinese NomBank corpus shows that our tree kernel based method on D-CPT performs significantly better than other tree kernel-based ones and achieves comparable performance with the state-of-the-art feature-based ones. This indicates the effectiveness of the novel D-CPT structure in representing various kinds of dependency relations in a CPT-style structure and our tree kernel based method in exploring the novel D-CPT structure. This also illustrates that the kernel-based methods are competitive and they are complementary with the feature- based methods on SRL.展开更多
In this papers we examine the issue of learning multiple predicates from given training examples. A proposed MPL-CORE algorithm efficiently induces Horn clauses from examples and background knowledge by employing a si...In this papers we examine the issue of learning multiple predicates from given training examples. A proposed MPL-CORE algorithm efficiently induces Horn clauses from examples and background knowledge by employing a single predicate learning module CORE. A fast failure mechanism is also proposed which contributes learning efficiency and learnability to the algorithm. MPL-CORE employs background knowledge that can be represented in intensional (Horn clauses) or extensional (ground atoms) forms during its learning process. With the fast failure mechanism, MPL-CORE outperforms previous multiple predicate learning systems in both the computational complexity and learnability.展开更多
Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key...Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key can be tampered by physical attacks on the device,the security of the scheme becomes totally unclear.In this work,we investigate predicate encryption(PE),a powerful encryption primitive,in the setting of tampering attacks.First,we show that many existing frameworks to construct PE are vulnerable to tampering attacks.Then we present a new security notion to capture such attacks.Finally,we take Attrapadung’s framework in Eurocrypt’14 as an example to show how to"compile"these frameworks to tampering resilient ones.Moreover,our method is compatible with the original pair encoding schemes without introducing any redundancy.展开更多
A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The ...A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.展开更多
Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key...Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key can be tampered by physical attacks on the device,the security of the scheme becomes totally unclear.In this work,we investigate predicate encryption(PE),a powerful encryption primitive,in the setting of tampering attacks.First,we show that many existing frameworks to construct PE are vulnerable to tampering attacks.Then we present a new security notion to capture such attacks.Finally,we take Attrapadung’s framework in Eurocrypt’14 as an example to show how to“compile"these frameworks to tampering resilient ones.Moreover,our method is compatible with the original pair encoding schemes without introducing any redundancy.展开更多
Frege argued that a predicate was a functional expression and the reference of it a concept, which as a predicative function had one or more empty places and was thus incomplete. Frege's view gives rise to what has b...Frege argued that a predicate was a functional expression and the reference of it a concept, which as a predicative function had one or more empty places and was thus incomplete. Frege's view gives rise to what has been known as the paradox of the concept "horse." In order to resolve this paradox, I argue for an opposite view which retains the point that a predicate is a function, i.e. that a predicative function is complete in a sense. Specifically speaking, a predicate performing the function of a predicate has at least one empty place and has no reference, while a predicate performing the function of a subject does not have any empty place but does have a reference. Frege not only regarded a concept with one or more empty places as the reference of a predicate but also took a set of objects without any empty place to be the extension of a concept with one or more empty places. Thus, it presents a complex relationship between the reference of a predicate and its corresponding extension, leading to disharmony in his theory. I argue that this is because there is a major defect in Frege's theory of meaning, namely the neglect of common names. What he called extensions of concepts are actually extensions of common names, and the references of predicates and the extensions of common names have a substantial difference despite being closely related.展开更多
English and Chinese belong to different language families,employing two distinct syntactic systems.English is subject-prominent,following the pattern of subject first,then predicate;while Chinese is topic-prominent,sh...English and Chinese belong to different language families,employing two distinct syntactic systems.English is subject-prominent,following the pattern of subject first,then predicate;while Chinese is topic-prominent,showing much flexibility in word arrangement as well as the necessity of subject and predicate.展开更多
The subjunctive mood is one of the most difficult English grammar items for most English learners. In this thesis,the author discusses the usage of the subjunctive mood in English,especially its usage in English subor...The subjunctive mood is one of the most difficult English grammar items for most English learners. In this thesis,the author discusses the usage of the subjunctive mood in English,especially its usage in English subordinate clauses. At the same time,the author provides a lot of examples. In the author's opinion,as long as the English learners find out the rules of it and practice it more,they will definitely grasp the subjunctive mood and use it correctly and skillfully.展开更多
The pozzolanic activity of coal gangue, which is calcining at 500 to 1 000 ℃, differs distinctly. The simplex-centroid design with upper and lower bounds of component proportion is adopted to study the compressive st...The pozzolanic activity of coal gangue, which is calcining at 500 to 1 000 ℃, differs distinctly. The simplex-centroid design with upper and lower bounds of component proportion is adopted to study the compressive strength of mortars made with ternary blends of cement, activated coal gangue and fly ash. Based on the results of a minimum of seven design points, three special cubic polynomial models are used to establish the strength predicating equations at different ages for mortars. Five experimental checkpoints were also designed to verify the precision of the equations. The most frequent errors of the predicted values are within 3%. A simple and practical way is provided for determining the optimal proportion of two admixtures when they are used in concrete.展开更多
In this paper, a formal approach based on predicate logic is proposed for representing and reasoning of trusted computing models. Predicates are defined to represent the characteristics of the objects and the relation...In this paper, a formal approach based on predicate logic is proposed for representing and reasoning of trusted computing models. Predicates are defined to represent the characteristics of the objects and the relationship among these objects in a trusted system according to trusted computing specifications. Inference rules of trusted relation are given too. With the semantics proposed, some trusted computing models are formalized and verified, which shows that Predicate calculus logic provides a general and effective method for modeling and reasoning trusted computing systems.展开更多
In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about...In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about uniform co-identical truthand uniform co-satisfiability.Thus some theorems in the book“A Course inMathematical Logic”,written by J.L.Bell and M.Machover,are corrected.展开更多
文摘SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is predicate data flow diagram (PDFD). In order to eliminate the ambiguity of predicate data flow diagrams and their associated textual specifications, a formalization of the syntax and semantics of predicate data flow diagrams is necessary. In this paper we use Z notation to define an abstract syntax and the related structural constraints for the PDFD notation, and provide it with an axiomatic semantics based on the concept of data availability and functionality of predicate operation. Finally, an example is given to establish functionality consistent decomposition on hierarchical PDFD (HPDFD).
基金National Natural Science Foundation of China (No. 60875034)Spanish Ministry of Education and Science Fund,Spain (No.TIN-2009-0828)Spanish Regional Government (Junta de Andalucia) Fund,Spain (No. P08-TIC-3548)
文摘Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.
文摘In the current biomedical data movement, numerous efforts have been made to convert and normalize a large number of traditional structured and unstructured data (e.g., EHRs, reports) to semi-structured data (e.g., RDF, OWL). With the increasing number of semi-structured data coming into the biomedical community, data integration and knowledge discovery from heterogeneous domains become important research problem. In the application level, detection of related concepts among medical ontologies is an important goal of life science research. It is more crucial to figure out how different concepts are related within a single ontology or across multiple ontologies by analysing predicates in different knowledge bases. However, the world today is one of information explosion, and it is extremely difficult for biomedical researchers to find existing or potential predicates to perform linking among cross domain concepts without any support from schema pattern analysis. Therefore, there is a need for a mechanism to do predicate oriented pattern analysis to partition heterogeneous ontologies into closer small topics and do query generation to discover cross domain knowledge from each topic. In this paper, we present such a model that predicates oriented pattern analysis based on their close relationship and generates a similarity matrix. Based on this similarity matrix, we apply an innovated unsupervised learning algorithm to partition large data sets into smaller and closer topics and generate meaningful queries to fully discover knowledge over a set of interlinked data sources. We have implemented a prototype system named BmQGen and evaluate the proposed model with colorectal surgical cohort from the Mayo Clinic.
文摘Respectively belonging to different language families,English and Chinese naturally have many differences in morphology and syntax.This paper intends to give a contrastive analysis of subject and predicate in English and Chinese,focusing on differences of subject and predicate usages in the two languages,and the problems they cause for Chinese students in English learning and translation.
文摘This paper described an approach to make inferences on Chinese information using first order predicate logic, which could be used in the semantic query of Chinese. The predicates of the method were derived from the natural language using rule based LFT, the axiom set was generated by extracting lexicon knowledge from HowNet, and the first order predicate inferences were made through symbol connection of center words. After all these were done, the evaluation and possible improvements of the method were provided. The experiment result shows a higher precision rate than that traditional methods can reach.
文摘A method to model and analyze the hybrid systems is presented. The time to be considered in the plant is taken as an explicit parameter through the constrained predicated net (CPN). The CPN's basic structure is a Petri net with predicated transition. All components of the net are expressed by annotation which is defined on rational set Q. The analysis method for the plant is interval temporal logic represented by Petri nets. This paper combines the above two methods to synthesize the hybrid system, gives a simple and clear expression of the expected action of the studied plant.
文摘Cognitive grammar,as a linguistic theory that attaches importance to the relationship between language and thinking,provides us with a more comprehensive way to understand the structure,semantics and cognitive processing of noun predicate sentences.Therefore,under the framework of cognitive grammar,this paper tries to analyze the semantic connection and cognitive process in noun predicate sentences from the semantic perspective and the method of example theory,and discusses the motivation of the formation of this construction,so as to provide references for in-depth analysis of the cognitive laws behind noun predicate sentences.
基金Supported by the National Natural Science Foundation of China under Grant Nos.61331011 and 61273320the National High Technology Research and Development 863 Program of China under Grant No.2012AA011102the Natural Science Foundation of Jiangsu Provincial Department of Education under Grant No.10KJB520016
文摘This paper explores a tree kernel based method for semantic role labeling (SRL) of Chinese nominal predicates via a convolution tree kernel. In particular, a new parse tree representation structure, called dependency-driven constituent parse tree (D-CPT), is proposed to combine the advantages of both constituent and dependence parse trees. This is achieved by directly representing various kinds of dependency relations in a CPT-style structure, which employs dependency relation types instead of phrase labels in CPT (Constituent Parse Tree). In this way, D-CPT not only keeps the dependency relationship information in the dependency parse tree (DPT) structure but also retains the basic hierarchical structure of CPT style. Moreover, several schemes are designed to extract various kinds of necessary information, such as the shortest path between the nominal predicate and the argument candidate, the support verb of the nominal predicate and the head argument modified by the argument candidate, from D-CPT. This largely reduces the noisy information inherent in D-CPT. Finally, a convolution tree kernel is employed to compute the similarity between two parse trees. Besides, we also implement a feature-based method based on D-CPT. Evaluation on Chinese NomBank corpus shows that our tree kernel based method on D-CPT performs significantly better than other tree kernel-based ones and achieves comparable performance with the state-of-the-art feature-based ones. This indicates the effectiveness of the novel D-CPT structure in representing various kinds of dependency relations in a CPT-style structure and our tree kernel based method in exploring the novel D-CPT structure. This also illustrates that the kernel-based methods are competitive and they are complementary with the feature- based methods on SRL.
文摘In this papers we examine the issue of learning multiple predicates from given training examples. A proposed MPL-CORE algorithm efficiently induces Horn clauses from examples and background knowledge by employing a single predicate learning module CORE. A fast failure mechanism is also proposed which contributes learning efficiency and learnability to the algorithm. MPL-CORE employs background knowledge that can be represented in intensional (Horn clauses) or extensional (ground atoms) forms during its learning process. With the fast failure mechanism, MPL-CORE outperforms previous multiple predicate learning systems in both the computational complexity and learnability.
基金This work was supported in part by National Natural Science Foundation of China(No.61632020,61472416,61772520)National key research and development program of China(No.2017YFB0802705)+1 种基金Key Research Project of Zhejiang Province(No.2017C01062)Fundamental Theory and Cutting-edge Technology Research Program of Institute of Information Engineering,CAS(No.Y7Z0321102).
文摘Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key can be tampered by physical attacks on the device,the security of the scheme becomes totally unclear.In this work,we investigate predicate encryption(PE),a powerful encryption primitive,in the setting of tampering attacks.First,we show that many existing frameworks to construct PE are vulnerable to tampering attacks.Then we present a new security notion to capture such attacks.Finally,we take Attrapadung’s framework in Eurocrypt’14 as an example to show how to"compile"these frameworks to tampering resilient ones.Moreover,our method is compatible with the original pair encoding schemes without introducing any redundancy.
文摘A modal logic for describing temporal as well as spatial properties of mobileprocesses, expressed in the asynchronous π-calculus, is presented. The logic has recur-sive constructs built upon predicate-variables. The semantics of the logic is establishedand shown to be monotonic, thus guarantees the existence of fixpoints. An algorithm isdeveloped to automatically check if a mobile process has properties described as formulasin the logic. The correctness of the algorithm is proved.
基金supported in part by National Natural Science Foundation of China(No.61632020,61472416,61772520)National key research and development program of China(No.2017YFB0802705)+1 种基金Key Research Project of Zhejiang Province(No.2017C01062)Fundamental Theory and Cutting-edge Technology Research Program of Institute of Information Engineering,CAS(No.Y7Z0321102).
文摘Many real world attacks often target the implementation of a cryptographic scheme,rather than the algorithm itself,and a system designer has to consider new models that can capture these attacks.For example,if the key can be tampered by physical attacks on the device,the security of the scheme becomes totally unclear.In this work,we investigate predicate encryption(PE),a powerful encryption primitive,in the setting of tampering attacks.First,we show that many existing frameworks to construct PE are vulnerable to tampering attacks.Then we present a new security notion to capture such attacks.Finally,we take Attrapadung’s framework in Eurocrypt’14 as an example to show how to“compile"these frameworks to tampering resilient ones.Moreover,our method is compatible with the original pair encoding schemes without introducing any redundancy.
文摘Frege argued that a predicate was a functional expression and the reference of it a concept, which as a predicative function had one or more empty places and was thus incomplete. Frege's view gives rise to what has been known as the paradox of the concept "horse." In order to resolve this paradox, I argue for an opposite view which retains the point that a predicate is a function, i.e. that a predicative function is complete in a sense. Specifically speaking, a predicate performing the function of a predicate has at least one empty place and has no reference, while a predicate performing the function of a subject does not have any empty place but does have a reference. Frege not only regarded a concept with one or more empty places as the reference of a predicate but also took a set of objects without any empty place to be the extension of a concept with one or more empty places. Thus, it presents a complex relationship between the reference of a predicate and its corresponding extension, leading to disharmony in his theory. I argue that this is because there is a major defect in Frege's theory of meaning, namely the neglect of common names. What he called extensions of concepts are actually extensions of common names, and the references of predicates and the extensions of common names have a substantial difference despite being closely related.
文摘English and Chinese belong to different language families,employing two distinct syntactic systems.English is subject-prominent,following the pattern of subject first,then predicate;while Chinese is topic-prominent,showing much flexibility in word arrangement as well as the necessity of subject and predicate.
文摘The subjunctive mood is one of the most difficult English grammar items for most English learners. In this thesis,the author discusses the usage of the subjunctive mood in English,especially its usage in English subordinate clauses. At the same time,the author provides a lot of examples. In the author's opinion,as long as the English learners find out the rules of it and practice it more,they will definitely grasp the subjunctive mood and use it correctly and skillfully.
基金The National Basic Research Program of China (973Program)(No2000CB610703)
文摘The pozzolanic activity of coal gangue, which is calcining at 500 to 1 000 ℃, differs distinctly. The simplex-centroid design with upper and lower bounds of component proportion is adopted to study the compressive strength of mortars made with ternary blends of cement, activated coal gangue and fly ash. Based on the results of a minimum of seven design points, three special cubic polynomial models are used to establish the strength predicating equations at different ages for mortars. Five experimental checkpoints were also designed to verify the precision of the equations. The most frequent errors of the predicted values are within 3%. A simple and practical way is provided for determining the optimal proportion of two admixtures when they are used in concrete.
基金Supported by the National High-Technology Re-search and Development Program ( 863 Program)China(2004AA113020)
文摘In this paper, a formal approach based on predicate logic is proposed for representing and reasoning of trusted computing models. Predicates are defined to represent the characteristics of the objects and the relationship among these objects in a trusted system according to trusted computing specifications. Inference rules of trusted relation are given too. With the semantics proposed, some trusted computing models are formalized and verified, which shows that Predicate calculus logic provides a general and effective method for modeling and reasoning trusted computing systems.
文摘In this paper,the authors point out and demonstrate the difference of theconcepts concerning co-satisfiable and co-valid between one first-order language andtwo first-order languages,and put forward the concepts about uniform co-identical truthand uniform co-satisfiability.Thus some theorems in the book“A Course inMathematical Logic”,written by J.L.Bell and M.Machover,are corrected.