Unification in Abelian Semigroups

Unification in equational theories, i.e. solving of equations in varieties, is a basic operation in Computational Logic, in Artificial Intelligence (AI) and in many applications of Computer Science. In particular the unification of terms in the presence of an associative and commutative f unction, i.e. solving of equations in Abelian Semigroups, turned out to be of practical relevance for Term Rewriting Systems, Automated Theorem Provers and many AI-programming languages. The observation that unification under associativity and commutativity reduces to the solution of certain linear diophantine equations is the basis for a complete and minimal unification algorithm. The set of most general unifiers is closely related to the notion of a basis for the linear solution space of these equations. These results are extended to unification in free term algebras combined with Abelian Semigroups

Concept logics

Concept languages (as used in BACK, KL-ONE, KRYPTON, LOOM) are employed as knowledge representation formalisms in Artificial Intelligence. Their main purpose is to represent the generic concepts and the taxonomical hierarchies of the domain to be modeled. This paper addresses the combination of the fast taxonomical reasoning algorithms (e.g. subsumption, the classifier etc.) that come with these languages and reasoning in first order predicate logic. The interface between these two different modes of reasoning is accomplished by a new rule of inference, called constrained resolution. Correctness, completeness as well as the decidability of the constraints (in a restricted constraint language) are shown

Opening the AC-Unification Race

This note reports about the implementation of AC-unification algorithms, based on the variable-abstraction method of Stickel and on the constant-abstraction method of Livesey, Siekmann, and Herold. We give a set of 105 benchmark examples and compare execution times for implementations of the two approaches. This documents for other researchers what we consider to be the state-of-the-art performance for elementary AC-unification problems

Isolation, Cloning and Structural Characterisation of Boophilin, a Multifunctional Kunitz-Type Proteinase Inhibitor from the Cattle Tick

Inhibitors of coagulation factors from blood-feeding animals display a wide variety of structural motifs and inhibition mechanisms. We have isolated a novel inhibitor from the cattle tick Boophilus microplus, one of the most widespread parasites of farm animals. The inhibitor, which we have termed boophilin, has been cloned and overexpressed in Escherichia coli. Mature boophilin is composed of two canonical Kunitz-type domains, and inhibits not only the major procoagulant enzyme, thrombin, but in addition, and by contrast to all other previously characterised natural thrombin inhibitors, significantly interferes with the proteolytic activity of other serine proteinases such as trypsin and plasmin. The crystal structure of the bovine α-thrombin·boophilin complex, refined at 2.35 Å resolution reveals a non-canonical binding mode to the proteinase. The N-terminal region of the mature inhibitor, Q16-R17-N18, binds in a parallel manner across the active site of the proteinase, with the guanidinium group of R17 anchored in the S1 pocket, while the C-terminal Kunitz domain is negatively charged and docks into the basic exosite I of thrombin. This binding mode resembles the previously characterised thrombin inhibitor, ornithodorin which, unlike boophilin, is composed of two distorted Kunitz modules. Unexpectedly, both boophilin domains adopt markedly different orientations when compared to those of ornithodorin, in its complex with thrombin. The N-terminal boophilin domain rotates 9° and is displaced by 6 Å, while the C-terminal domain rotates almost 6° accompanied by a 3 Å displacement. The reactive-site loop of the N-terminal Kunitz domain of boophilin with its P1 residue, K31, is fully solvent exposed and could thus bind a second trypsin-like proteinase without sterical restraints. This finding explains the formation of a ternary thrombin·boophilin·trypsin complex, and suggests a mechanism for prothrombinase inhibition in vivo

Unification algebras: an axiomatic approach to unification, equation solving and constraint solving

Traditionally unification is viewed as solving an equation in an algebra given an explicit construction method for terms and substitutions. We abstract from this explicit term construction methods and give a set of axioms describing unification algebras that consist of objects and mappings, where objects abstract terms and mappings abstract substitutions. A unification problem in a given unification algebra is the problem to find mappings for a system of equations 〈si = ti|i ∈ I〉, where si and ti are objects, such that si and ti are mapped onto the same object. Typical instances of unification algebras and unification problems are: Term unification with respect to equational theories and sorts, standard equation solving in mathematics, unification in the λ-calculus, constraint solving, disunification, and unification of rational terms. Within this framework we give general purpose unification rules that can be used in every unification algorithm in unification algebras. Furthermore we demonstrate the use of this framework by investigating the analogue of syntactic unification and unification of rational terms

Reasoning with Assertions and Examples

The hallmark of traditional Artificial Intelligence (AI) research is the symbolic representation and processing of knowledge. This is in sharp contrast to many forms of human reasoning, which to an extraordinary extent, rely on cases and (typical) examples. Although these examples could themselves be encoded into logic, this raises the problem of restricting the corresponding model classes to include only the intended models. There are, however, more compelling reasons to argue for a hybrid representation based on assertions as well as examples. The problems of adequacy, availability of information, compactness of representation, processing complexity, and last but not least, results from the psychology of human reasoning, all point to the same conclusion: Common sense reasoning requires different knowledge sources and hybrid reasoning principles that combine symbolic as well as semantic-based inference. In this paper we address the problem of integrating semantic representations of..

Analogical Reasoning with a Hybrid Knowledge Base

this paper, we address the questions of the availability of certain forms of knowledge and of the efficiency of inferences by suggesting an approach to justified analogical reasoning. Starting from a logically oriented view of standard analogical reasoning, we review some empirical results on human concept representation in order to show how to use hybridly represented knowledge for mechanical analogical reasoning as well. The essence of our approach is to augment the propositional knowledge representation system by a non-propositional part consisting of concept structures which may have directly represented instances as elements. The necessary information for analogical reasoning is then extracted from either part of the knowledge representation system. In other words, the general idea is to incorporate the particular non-propositional part of a hybrid knowledge representation system into a traditional reasoning system such that it can be extended by inference rules using information extracted from both knowledge representation subsystems. Thus the general framework and foundational importance of logic will remain unquestioned. Justified Analogical Reasonin

Analogical Reasoning with a Hybrid Knowledge Base

this paper, we address the questions of the availability of certain forms of knowledge and of the efficiency of inferences by suggesting an approach to justified analogical reasoning. Starting from a logically oriented view of standard analogical reasoning, we review some empirical results on human concept representation in order to show how to use hybridly represented knowledge for mechanical analogical reasoning as well. The essence of our approach is to augment the propositional knowledge representation system by a non-propositional part consisting of concept structures which may have directly represented instances as elements. The necessary information for analogical reasoning is then extracted from either part of the knowledge representation system. In other words, the general idea is to incorporate the particular non-propositional part of a hybrid knowledge representation system into a traditional reasoning system such that it can be extended by inference rules using information extracted from both knowledge representation subsystems. Thus the general framework and foundational importance of logic will remain unquestioned. Justified Analogical Reasonin