D. McAllester and R. Givan. Taxonomic Syntax for First-Order Inference. Journal of the ACM, 40(2), Apr. 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....satisfiability of INES constraints with negation in the finite tree case. The results in [11] do not include any of the results presented here since they use as an explicit prerequisite the fact that satisfiability of INES constraints is decidable. Tarskian Set Constraints. MacAllester and Givan [21] give a cubic algorithm which decides satisfiability for a class of Tarskian set constraints [22] and which also contains a non disjointness constraint. Apart from this syntactic similarity, the two satisfiability problems are rather different problems since Tarskian set constraints are not ....

D. McAllester and R. Givan. Taxonomic Syntax for First-Order Inference. Journal of the ACM, 40(2), Apr. 1993.

....connectives and V. The rule set B expresses some, but not all, of the inferential properties of these connectives. The rule set B can be viewed as a (somewhat obscure) characterization of unit resolution, or as a specification of the Boolean constraint propagation mechanism described in [McAllester, 1989]. The inference relation generated by these rules is linear time decidable. Yet, if the above inference rules are augmented by a simple case analysis sequent rule then the rules become complete for Boolean inference. As another example of a set of inference rules, consider the following rules for ....

....involve quantification. Even without quantifiers, a set of rules can still generate an undecidable or intractable inference relation. On the other hand, the presence of quantifiers does not necessarily prevent tractability. Tractable inference relations involving quan tiffcation are discussed in [McAllester, 1989] and [McAllester et al. 1989] A more general notion of locality will be needed to construct a procedure for automatically recognizing tractability in rule sets that involve quantification. Definition: A well formed expression of kind formula will be called a formula. Definition: An inference ....

[Article contains additional citation context not shown here]

D. McAllester, R. Givan, and T. Fatima. Taxono- mic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reason- ing, pages 289-300, 1989.

....basic definitions. Propositional logic is another example of a language in which reasoning is very efficient. In propositional logic, there is a decision procedure. But, in propositional logic, it is impossible even to express the notion of every or some in a general way. David McAllester [58, 59, 86, 87] has developed languages that are more expressive than first order logic and for which the subset of the language for which there is a decision procedure properly contains the subset of first order logic for which there is a decision procedure. This is a great advantage. The disadvantages include ....

....language description of a proof once it is finished. Boyer, Moore and Kaufmann s NQTHM prover communicates with the user largely in English although formulas and terms in the formal language are not translated [38] David McAllester developed a formal language that more closely resembles English [84, 87]. The proof system, Ontic, checks proofs in this language. Chapter 8 Conclusion one could be too conservative in estimating the potentialities of machines in theorem proving. Hao Wang. 1960 [116] In this chapter, we summarize the new results presented in this dissertation and ....

David McAllester and Robert Givan. Taxonomic syntax for first order inference. Journal of the ACM, 40(2):246--283, April 1993.

....but which have some overlap with them (as remarked in [MG92] These languages are interesting in the context of description logics since they have polynomial time algorithms for solving a subsumption like problem. Two of McAllester s languages are examined, one with a firstorder taxonomic syntax [MGF89, MG93] and the other with a Montagovian syntax [GMS91, MG92] Both languages are equivalent to first order logic. Taxonomic syntax consists of taxonomic terms and formulas, where taxonomic terms denote sets of objects (just as concepts do) and formulas state relationships between terms (just as ....

D. McAllester, B. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of 13 Knowledge Representation and Reasoning, pages 289-- 300, 1989.

....but which have some overlap with them (as remarked in [MG92] These languages are interesting in the context of description logics since they have polynomial time algorithms for solving a subsumption like problem. Two of McAllester s languages are examined, one with a firstorder taxonomic syntax [MGF89, MG93] and the other with a Montagovian syntax [GMS91, MG92] Both languages are equivalent to first order logic. Taxonomic syntax consists of taxonomic terms and formulas, where taxonomic terms denote sets of objects (just as concepts do) and formulas state relationships between terms (just as ....

D. McAllester and R. Givan. Taxonomic syntax for first order inference. Journal of the Association for Computing Machinery, 40:246--283, 1993.

....set answering function can be considered as an application of the basic idea of their scheme to taxonomy reasoning under the restriction that the arity of function is one. DOT enhances the inference capability of the system by using set operations and closure property of regular sets. McAllester[17] shows polynomial time algorithms for taxonomy reasoning. His systems are semantically more expressive than DOT. DOT enhances (possibly infinite) set operations such as set at a time query, specification of knowledge, and set operations. Query languages using dot notations have been used in ....

McAllester, D. and Givan, B., "Taxonomic Syntax for First Order Inference", Journal of the ACM, Vol.40, No.2, pp.246-283, 1993.

....R. Givan, C. Witty and D. Kozen [14] liberalized the notions of set constraints to so called Tarskian set constraints over arbitrary firstorder domain, with a link to modal logics. Early work on Tarskian set constraints by R. Givan and D. McAllester stemmed from the work on artificial intelligence [9, 13]. D. McAllester, R. Givan, C. Witty and D. Kozen [14] gave a complexity analysis of systems of Tarskian set constraints depending on various parameters. They proved that the satisfiability problem for set constraints with deterministic operators of arbitrary arity (functions and constants) ....

D. A. McAllester and R. Givan. Taxonomic syntax for first order inference. Journal of ACM, 40:346--283, 1993.

....Based on our earlier experience, described in the introduction, however, we expect this restriction to be a significant limitation. The basic idea of limiting the depth of assumption nesting goes back at least to Access Limited Logic (ALL) Crawford Kuipers 1989] and Socratic sequent systems [McAllester, Givan, Fatima 1989]. The results reported here grew out of our attempts to semantically characterize ALL. The first attempt to define a semantics for such limited inference is Dalal s recent work [Dalal 1996b] Dalal s semantics assigns real numbers in the range [0,1] to all variables in the theory, and assigns 1 ....

McAllester, D.; Givan, R.; and Fatima, T. 1989. Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning (KR'89), 289--300.

....ideas on visual environments are introduced. As shown in Section 2, the intuitive interpretation of diagrams is based on sets and set inclusion. Set terms and set term inclusions provide an alternative syntax for FOL that is very near to the taxonomic and Montagovian syntax for FOL in [22] and [23] respectively. This non standard syntax for FOL possesses benefits other than facilitating visualization as shown here. As McAllester claims in [22, 23] it has a closer connection with natural language than conventional FOL syntax and it may make first order inference more efficient. 5 ....

....terms and set term inclusions provide an alternative syntax for FOL that is very near to the taxonomic and Montagovian syntax for FOL in [22] and [23] respectively. This non standard syntax for FOL possesses benefits other than facilitating visualization as shown here. As McAllester claims in [22, 23] it has a closer connection with natural language than conventional FOL syntax and it may make first order inference more efficient. 5 Conclusions and Work in Progress The visual language presented in this paper is mainly a representation for a subset of FOL well known in declarative ....

David McAllester, Robert Givan, and T. Fatima. Taxonomic Syntax for First Order Inference. Journal of the ACM, 40(2):246--283, 1993.

.... Computational Complexity of Taxonomic Inference Radford Neal December, 1989 McAllester, Given, and Fatima [10] have developed a procedure for infering taxonomic relationships between classes defined by predicates and relations. Their decision procedure runs in O(n 3 ) time and O(n 2 ) space on a sequential randomaccess machine (RAM) I have investigated the computational complexity of this inference ....

....that the decision procedure for Montague literals might explain some aspects of natural language. A Taxonomic Inference System The system for taxonomic inference that I will discuss is a subset of a more general system of inference for taxonomic literals described by McAllester, et al. [10]. Their system permits statements that one set is included in another, that two sets have a non null intersection, that a set is non empty, and that a set contains no more than one element, as well as the negations of such statements. The system I will describe allows only positive assertions that ....

[Article contains additional citation context not shown here]

McAllester, D., Givan, B. and Fatima, T. (1989) Taxonomic syntax for first order inference, Proceeding of the First International Conference on Principles of Knowledge Representation and Reasoning, pp. 289-300.

....Any variable which is not restricted in this way is said to be unrestricted. The next section will make more clear why the restrictions on syntax supplied in definition 2 are needed. It is worth noting in passing that set expressions for first order predicate calculus have also been introduced in [3] but in a different form and for different purposes. 3 Mapping Prolog to the Refinement Language Section 2 introduced the basic notation for the refinement language. The purpose of this section is to show how the language can be understood in terms of Prolog. To simplify our explanation, we shall ....

D. McAllester, B. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proceedings of KR-89, 1989.

....there has been growing interest in identifying tractable inference rules inference rules under which implication is decidable in polynomial time. One interesting result to come out of this work is that the power of tractable inference rules is dependent on the syntax of the language used [McAllester et al. 89] see also [McAllester, 90] p. 1115) Along these line, Shastri Ajjanagadde, 90] shows that, using a highly parallel implementation, certain queries can be answered in time proportional to the length of the shortest derivation of the query. Term subsumption languages (the current state of ....

McAllester, D., Givan, R., and Fatima, T. (1989). Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, Morgan Kaufmann, Los Altos, California, pp. 289300.

....Symbols the following diagram: human mortal To further exploit the properties of this diagrammatic formalism, we use a syntax where the composition of relations can be expressed in the same way as function composition. A similar syntax, called taxonomic syntax, was designed by McAllester in [10, 11]. In this type of syntax we have class terms (also set terms) referring to the fact that these terms constructed from predicates represent sets of elements. Actually, they can be seen as logical constrains over elements that implicitly determine a set. 2.1 Terms In our visual logic we have two ....

....whether we could visualize higher order logic, i.e. Prolog. As shown in Section 2, the intuitive interpretation of diagrams is based on sets and set inclusion. Set terms and set term inclusions provide an alternative syntax for FOL that is very near to McAllester s taxonomic syntax (see [10] and [11]) However, McAllester s work is directed towards the study of possible benefits of this non standard syntax for FOL, different than facilitating visualization as shown here. For instance as argued in [10] and [11] it may make first order inference more efficient, because of its close ....

[Article contains additional citation context not shown here]

David McAllester, Robert Givan, and T. Fatima. Taxonomic Syntax for First Order Inference. Journal of the ACM, 40(2):246--283, 1993.

....conclusions of specialized inferences. Furthermore sometimes it is also interesting to take into account specific non standard notations of first order sentences, which will serve both purposes, to facilitate readability of our logical assertions and improve the efficiency of logical deductions [14]. In this sense, one of the mainly used special deduction techniques is term rewriting, on which the operational semantics of functional and equational languages is based. Term rewriting techniques have turned out to be among the more successful approaches to equational theorem proving. Rewriting ....

D. McAllester, B. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proc. of the First Int. Conf. on Principles of Knowledge Representation and Reasoning, pages 289--300, 1989.

....indeterminate number of iterations of an operation. The induction rule is similar to the induction rule of propositional dy namic logic [Pratt, 19761, Harel, 19841, Kozen and Tiuryn, 19901. The language described here is also closely related to the knowledge representation language described in [McAllester et al. 1989]. The classical syntax for first order logic involves two grammatical categories formulas and terms. The knowledge representation language described here also involves two syntactic categories formulas and class expressions. Formulas denote truth values and class expressions denote sets. ....

D. McAllester, R. Givan, and T. Fatima. Taxonomic syn- tax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 289-300, 1989. To Appear in JACM.

....infers a strict superset of the theorems the other infers. we are especially interested in inferring properties that require expressive representation to state. The answer to this question proves very sensitive to the representation system used in inference. We draw on our previous work with McAllester(1993; 1992) to select a representation for program properties amenable to rapid inference. This representation derives from viewing properties as sets of program values a program has a property if the program returns a value in the corresponding set of values. Taking this view, program properties ....

McAllester, D., and Givan, R. 1993. Taxonomic syntax for first order inference. JACM 40(2):246--283. ftp.ai.mit.edu:/pub/users/dam/jacm1.ps.

....assigned. The relationship between inference and constraint propagation can be made explicit by characterizing constraint propagation processes in terms of inference rules. Boolean constraint propagation can be defined in terms of a certain (incomplete) set of inference rules for Boolean logic [ McAllester, 1989 ] Van Hentenryck also defines the various constraint propagation techniques used in Chip in terms of rules of inference. In fact, virtually any form of constraint propagation can be defined in terms of rules of inference. Constraint propagation inference rules are unusual, as rules of ....

....that do not correspond to any standard constraint propagation technique. For example, the inference rules that define BCP can be combined with the standard inference rules for equality, including the substitution of equals for equals, and the resulting rule set is still polynomial time decidable [ McAllester, 1989 ] In [ McAllester et al. 1989 ] it is argued that the power of tractable rule sets for first order inference is sensitive to the syntax in which formulas are expressed an alternative syntax based on taxonomic relationships between classes yields a more powerful tractable rule set. In [ ....

[Article contains additional citation context not shown here]

D. McAllester, R. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 289--300, 1989.

.... of the form s t which are derivable from E and where s and t appear in E (and hence x s and x t appear in P ) It can be shown that if s and t are terms appearing in E and s t is derivable from E then there exists a derivation of s t such that every term in that derivation appears in E [12, 9]. We now prove by induction on these local derivations that if s t is derivable from E then x s x t is derivable from P . We need to consider each inference rule in the definition of bimonotone reachability. In each case we can assume that terms appearing in the antecedent of the rule also ....

D. McAllester and R. Givan, "Taxonomic syntax for first order inference", JACM, 40(2):246--283, April 1993. (ftp.ai.mit.edu:/pub/users/dam/jacm1.ps)

....indeterminate number of iterations of an operation. The induction rule is similar to the induction rule of propositional dynamic logic [Pratt, 1976] Harel, 1984] Kozen and Tiuryn, 1990] The language described here is also closely related to the knowledge representation language described in [McAllester et al. 1989]. The classical syntax for first order logic involves two grammatical categories formulas and terms. The knowledge representation language described here also involves two syntactic categories formulas and class expressions. Formulas denote truth values and class expressions denote sets. ....

D. McAllester, R. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 289--300, 1989. To Appear in JACM.

....Goldblatt [ Goldblatt, 1989 ] See also [ Kozen, 1993 ] 4 which in turn subsumes most features of the concept languages developed for AI applications. In spite of the apparent naturality of Tarskian set constraints their computational properties have not been widely studied. It is shown in [McAllester and Givan, 1993] that satisfiability of nonrecursive Tarskian set constraints not involving Boolean operations is decidable in cubic time (assuming unit time hash table operations) The results of this paper are summarized in the following table. We categorize Tarskian set constraint satisfiability problems by ....

.... 1984] The positive entailment problem for L( can be shown to be NP complete (we leave this as an exercise for the reader) It is known that satisfiability of Tarskian set constraints not involving Boolean operations or recursion, but with function symbols, is decidable in polynomial time [McAllester and Givan, 1993] . This implies that the positive entailment problem for L(3) is decidable in polynomial time. By duality arguments given below this implies that the positive entailment problem for L(2) is also decidable in polynomial time. To our knowledge the difficulty of the positive entailment problem for ....

D. McAllester and R. Givan. Taxonomic syntax for first order inference. JACM, 40(2):246--283, April 1993. internet file ftp.ai.mit.edu:/pub/dam/jacm1.ps.

....symbol. is restricted so that X can only occur inside an even number of negation symbols in C. We consider finite sets of constraints of the form or . In spite of the apparent naturality of Tarskian set constraints, their computational properties have not been widely studied. It is shown in (McAllester and Givan, 1993) that satisfiability of nonrecursive Tarskian set constraints not involving Boolean operations is decidable in cubic time (assuming unit time hash table operations) It is shown in (Givan and McAllester, 1992) that satisfiability of constraints on expressions involving meets, joins, and monotone ....

.... be shown to be NP complete (we leave this as an exercise for the reader) It is known that satisfiability of Tarskian set constraints not involving Boolean operations or recursion, but with both deterministic and nondeterministic operation symbols of all arities, is decidable in polynomial time (McAllester and Givan, 1993). This implies that the positive entailment satisfiability problem for is decidable in polynomial time. By duality arguments given below this implies that the problem for is also decidable in polynomial time. To our knowledge the difficulty of the positive entailment problem for other combinations ....

McAllester and Givan, 1993 [27] McAllester, D. and Givan, R. (1993), Taxonomic syntax for first order inference, J. ACM, 40(2), 246--283. Also available at http://www.ece.purdue.edu/ ~givan/papers/jacm1.ps.

.... from the edges in E using the inference rules of transitivity and monotonicity where monotonicity states that if n 1 n 2 then f(n 1 ) f(n 2 ) It is possible to show that one need only derive arcs of the form s t where s and t are expressions of the form n or f(n) that appear in arcs in E [11, 8]. So, as in transitive closure, the set of derivable arcs can be enumerated in a naive way in cubic time. But unlike transitive closure, no sub cubic algorithm is known. As examples of a monotone closure hardness results we given linear time reduction of monotone closure to control flow analysis ....

D. McAllester and R. Givan. Taxonomic syntax for first order inference. JACM, 40(2):246--283, April 1993. internet file ftp.ai.mit.edu:/pub/users/dam/jacm1.ps.

....system can be shorter than proofs in more traditional systems. However, because the rule set generating obvious sequents is local, the correctness of a proof can still be verified in polynomial time. Particular Socratic sequent systems for set theory and first order logic are described in [5] and [4]. It appears that the power of the local rule set in a Socratic sequent system can be enhanced through the use of a nonstandard syntax for first order logic. Aspects of the syntax of English under Mantague semantics have been used to construct particularly powerful general purpose local rule sets ....

....quantification. Even without quantifiers, a set of rules can still generate an undecidable or intractable inference relation. On the other hand, the presence of quantifiers does not necessarily prevent tractability. Tractable inference relations involving quantification are discussed in [5] and [4]. A more general notion of locality will be needed to construct a procedure for automatically recognizing tractability in rule sets that involve quantification. Definition: An expression of kind formula will be called a formula. Definition: An inference rule is an object of the form Psi 1 . ....

D. McAllester, R. Givan, and T. Fatima. Taxonomic syntax for first order inference. In Proceedings of the First International Conference on Principles of Knowledge Representation and Reasoning, pages 289--300, 1989. To Appear in JACM.

....addresses the clarity and conciseness achieved through nondeterminism, nondeterminism can also be motivated as a means of achieving greater automation. Nondeterminism can be viewed as an alternative syntax for first order terms and formulas the so called taxonomic syntax for first order logic [6]. Taxonomic syntax has significant advantages for automated reasoning it allows a larger fragment of the reasoning process to be handled by efficient type inference mechanisms. The use of taxonomic syntax is part of a larger program of basing inference procedures on nonstandard syntactic ....

....Ontic language. It would be particularly interesting to construct a verification system for this language using a metasystem such as Isabelle [10] Ideally any verification system for Ontic would take advantage of inference algorithms for taxonomic syntax such as those described in described in [6]. 2 Basic Ontic The Ontic language is presented here in stages. First, this section describes a strongly typed nondeterministic Lisp. Later sections extend the language with additional primitives providing all the expressive power of Zermelo Fraenkel set theory with the axiom of choice (ZFC) ....

[Article contains additional citation context not shown here]

D. McAllester and R. Givan. Taxonomic syntax for first order inference. JACM, 40(2):246--283, April 1993.

No context found.

McAllester, David and Robert Givan. 1989b. Taxonomic syntax for first order inference. A.I. Memo No. 1134, Massachusetts Institute of Technology, Cambridge, Massachusetts, June.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC