C. Walther. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217--224, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for sorts. Consequently, the computational mechanisms may change, which typically shows up in the unification procedure. One direction, which appeared with Eqlog [GM86] takes order sorted logic as base and employs order sorted unification [Gog78, GM87b, HV87, MGS89, SNGM89, SS85, SS89, Wal83, Wal85, Wal87, Wal88] This thesis generalizes this line of research by incorporating parametric polymorphism. The distinctive difference between order sorted types [Gog78, GM87a, SNGM89] and POStypes is that POS types can come with sort functions such as list or pair while order sorted types cannot. ....

C. Walther. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26:217--224, 1985.

....its own sort and supersorts as in Likes to eat(animal(bird(x) plant(y) and :Likes to eat(animal(u) plant(grain(v) then ordinary unification suffices to impose the sort constraints. Many sorted logic can be extremely effective (e.g. see Walther s solution of Schubert s Steamroller problem [33], a problem we also discuss in the next section) However, there are some important assumptions associated with its use. One is the assumption of the nonemptiness of the sorts used. P (x) and :P (x) are not contradictory if x s sort is empty. More restrictive in practice is the assumption that ....

....are much smaller than wolves. Wolves do not like to eat foxes or grains, while birds like to eat caterpillars but not snails. Caterpillars and snails like to eat some plants. Therefore there is an animal that likes to eat a grain eating animal. In reporting a solution to this problem, Walther [33] states, this problem became well known, since, in spite of its apparent simplicity, it turned out to be too hard for existing theorem provers because the search space is just too big. An English language solution to the problem is Every animal either likes to eat all plants or all animals ....

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Walther, C. A mechanical solution of Schubert's steamroller by many-sorted resolution. Proceedings of the AAAI-84 National Conference on Artificial Intelligence, Austin, Texas, August 1984, 330--334.

....have long been recognized as an important means of succinctly expressing inheritance relations. They are particularly valuable in the area of automated deduction because they can be built into the inference engine by means of order sorted unification, thus reducing the search space significantly [27]. This has sparked a lot of research on order sorted equational reasoning for first order terms (see, for example, 24] More recently there has been a drive towards the use of typed calculus for representing terms and formulae with bound variables [16, 20] Again, this is not only conceptually ....

C. Walther. A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26:217--224, 1985.

....data types whose elements are described by features as well as data types whose elements are described by constructors and shows the duality of the two approaches under the given initial algebra semantics. Furthermore, we present a unification algorithm that combines order sorted unification [27, 28] with term unification [1, 3] The paper is organized as follows. Section 2 formalizes signatures, interpretations and feature terms and shows that every feature term can be rewritten as a union of simple feature terms. Section 3 presents a relational language of set descriptions and shows that ....

....than general purpose mechanisms. Overstating it a little bit, we could say that predicate logic is to knowledge representation what Turing machines are to programming languages. For instance, if subsorts are added as a distinguished structure to predicate logic, order sorted unification [27, 28] replaces ordinary unification and leads to smaller search spaces. Feature terms obviously generalize sorts (which are in fact primitive feature terms) and can be integrated by allowing for containments x: s, where s is a feature term possibly containing variables. For inference, feature term ....

C. Walther. A mechanical solution of Schubert's steamroller by manysorted resolution. Artificial Intelligence, 26:217--224, 1985.

....Predicates and functions are also typed (according to the types of their arguments, and, for functions only, their results) The inference rules of the logic take into account that two terms can only match if there are appropriate subsort relationships between their sorts. Previous work in ai (Walther, 1984); Cohn, 1985) has shown these languages to have a number of advantages. These include the reduction of the number of axioms, the reduction of the length of logical formulae, a reduced search space during deduction, and increased human readability. Furthermore, sorts provide a natural form for ....

Walther, C. (1984). A mechanical solution of Schubert's steamroller by many-sorted resolution. In Proceedings of the fourth National Conference on Artificial Intelligence, pages 330--334, Austin, Texas. American Association for Artificial Intelligence.

....or inference steps in untyped systems. In automatic deduction systems, this has been found to provide a significant run time gain due to the fact that useless branches in the search space can be efficiently detected and pruned before the creation of expensive structural copies or binding frames (Walther 1985, 1988; Ait Kaci and Nasr 1986) In a constraint based linguistic theory such as HPSG, parsing and generation reduces to solving constraints. We allow constraints to be expressed by a feature logic analogue of definite clauses. The benefit of this approach is that it admits a natural and effective ....

Walther, C. (1985). A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217--224.

....concept. It allows to detect many common programming errors at compile time which otherwise may be difficult to locate. Additionally, in AI applications like theorem proving it has been shown that the introduction of types with subtypes may drastically reduce the search space of a problem (e.g. [Walther, 1985]) On the other hand, types should not burden the programmer or knowledge engineer with requiring a too narrow and strict discipline. Therefore, the type concept of PROTOS L covers user defined sorts, subsort relationships supporting multiple inheritance and parameterized sorts in the form of ....

C. Walther. A mechanical solution of Schubert's steamroller by manysorted resolution. Artificial Intelligence, 26:217--224, 1985.

....inheritance is semantically and pragmatically useful. Novel programming languages are being designed which allow the user to specify type hierarchies. Examples of these are class inheritance in Common Loops [9] and SmallTalk [12] flavor inheritance in ZetaLisp [20] subsorts in Theorem Proving [18, 19], type checking in Amber [10] Galileo [2] and more recently object oriented programming formulated as order sorted algebraic abstract data typing [11, 17] and David McAllester s work on boolean class expressions [14] In general, objects which are instance of classes organized in a partial ....

....than one superclass) such as ZetaLisp [20] or Smalltalk [12] use an ad hoc solution for combining class properties which depend on the temporal total order in which the classes are defined or appear in an expression. This is clearly semantically unclean and pragmatically hazardous. Other proposals [3, 19, 14] have formalized the concept of class inheritance in lattice theoretic terms. This captures the essential properties useful in practice for object oriented languages, and allows a better handling of class expressions for efficient implementation. e.g. given a taxonomy of objects a subsumption ....

Walther, C. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26 (1985) pp. 217--224.

....subsets of the domain have been used to represent information in a wide range of domains. A number of demonstrations have shown that deduction systems based on sorted logic can be much more efficient than their counterparts based on unsorted logic [Cohn, 1985; Ohlbach and Schmidt Schau , 1985; Walther, 1985; Frisch, 1986b; Walther, 1987; Stickel, 1986; Cohn, 1989] Though evidence has mounted, little has been done to examine closely how and why this improvement occurs nor have detailed measurements been made of how much speedup is obtained. This paper addresses these issues by comparing and ....

....of the sort theory and store them in an efficiently accessible data structure. 5 A number of studies have reported that a deduction system based on such a unification procedure can be more efficient than the corresponding unsorted system [Cohn, 1985; Ohlbach and Schmidt Schau , 1985; Walther, 1985; Frisch, 1986b; Walther, 1987; Stickel, 1986; Cohn, 1989] This should come as no surprise; after all, what we have essentially done is to relocate part of the deduction problem into the unification procedure and solve that part with a special purpose method table lookup rather than with a ....

[Article contains additional citation context not shown here]

Christoph Walther. A mechanical solution of Schubert's Steamroller by manysorted resolution. Artificial Intelligence, 26(2):217--224, 1985.

....A sorted logic is polymorphic if a function can have different result sorts, depending on the argument sorts. One motivation for sorts is, roughly speaking, that proofs can be kept at a more general level compared to unsorted logic, thus reducing the search space [ Cohn, 1985, Frisch, 1985, Walther, 1985 ] It has also been argued that deduction with sorts can be implemented more efficiently by specialized procedures [ Cohn, 1989 ] For example, for order sorted logics, there are efficient methods to find the greatest lower bound (glb) of two sorts in a sort hierarchy [ Ait Kaci et al. 1989, ....

Christoph Walther. A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217--224, 1985. This article was processed using the L a T E X macro package with LLNCS style

....Historically, sorts came from logic, where they were used to separate symbols into (usually disjoint) subdomains. Although sorts do not increase the expressive power of the logic, they may lead to clearer and more concise specifications; they also have been used to speed up automatic proofs [32]. Types , too, originate in logic [8] However their introduction into logic based programming languages is primarily due to the influence of functional and object oriented programming, where it has been shown that sufficiently rich polymorphic type systems would allow the user to write ....

C. Walther. A mechanical solution of Schubert's Steamroller by many-sorted resolution. Artificial Intelligence, 26:217--224, 1985.

.... exx7 is a situation calculus theorem developed by David Plaisted [Pla82] latinsq is the latin square problem from [Rob63] liar is the truthtellers and liars problem [LO85] salt is the salt and mustard problem from Lewis Carroll [LO85] The problem schubert is Schubert s steamroller [Wal84] The stack problem is a proof of a trivial property of push down stores. Problems 104 111 are pigeonhole problems from Pelletier s paper [Pel86] Problems 112 115 are implicational calculus theorems. The problem freuder is a constraint satisfaction problem taken from Freuder s paper [Fre78] ....

C. Walther. A mechanical solution of schubert's steamroller by many-sorted resolution. In Proceedings of the 4th National Conference on Artificial Intelligence, pages 330--334, 1984.

....[ Frisch and Page, 1990 ] parsing logical languages [ Frisch, 1986b ] and natural language processing [ Veronis, 1987 ] among other areas. Sorts have been shown to improve the efficiency of deductive systems (given the appropriate formulation of the problem at hand) in [ Cohn, 1985 ] Walther, 1985a ] Ohlbach and Schmidt Schau , 1985 ] Stickel, 1986 ] Cohn, 1989a ] and [ Abrams and Frisch, 1989 ] Walther [ 1985b ] examines sorted unification in the monomorphic case, allowing an infinite number of sorts, and shows how the existence and cardinality of a set of most general ....

Christoph Walther. A mechanical solution of Schubert's Steamroller by manysorted resolution. Artificial Intelligence, 26(2):217--224, 1985.

....A bibtex reference can be found in ftp.ai.mit.edu: pub dam dam.bib. 1 Introduction Schubert s steamroller is a well known challenge problem for automated reasoning systems [Cohn, 1989] Cohn, 1984] Stickel, 1985] Bibel et al. 1987] Davies, 1988] Oppacher and Suen, 1986] and [Walther, 1984]. All previous automated solutions of Schubert s steamroller have been based on search procedures procedures that search for proofs and which are not guaranteed to halt. In this paper we describe a different kind of solution to Schubert s steamroller a solution without search. Although ....

Christoph Walther. A mechanical solution of schubert's steamroller by many-sorted resolution. In Proceedings of AAAI-84, pages 330--334. Morgan Kaufmann Publishers, 1984.

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C. Walther. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217--224, 1985.

No context found.

C. Walther. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26(2):217--224, 1985.

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Walther, C. A mechanical solution of Schubert's steamroller by many-sorted resolution. Artificial Intelligence, 26 (1985) pp. 217--224.

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