A logic for constant-depth circuits

Consider a family of boolean circuitsC1,C2,...,Cn,..., constructed by some uniform, effective procedure operating on inputn. Such a procedure provides a concise representation of a family of parallel algorithms for computing boolean values. A formula of first-order logic may also be viewed as a concise representation of a family of parallel algorithms for evaluating boolean functions. The parallelism is implicit in the quantification (a formula [for all]x(x) is true if and only if each of the formulas(a) is true, and all these formulas can be checked simultaneously), and universes of different sizes give rise to boolean functions with different numbers of inputs (the boolean values of the formula's predicates on various combinations of elements of the universe). This note presents an extended first-order logic designed to be exactly equivalent in expressiveness to polynomialsize, constant-depth, unbounded-fan-in circuits constructed by Turing machines of bounded computational complexity.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24848/1/0000275.pd

A Multi-Engine Approach to Answer Set Programming

Answer Set Programming (ASP) is a truly-declarative programming paradigm proposed in the area of non-monotonic reasoning and logic programming, that has been recently employed in many applications. The development of efficient ASP systems is, thus, crucial. Having in mind the task of improving the solving methods for ASP, there are two usual ways to reach this goal: $(i)$ extending state-of-the-art techniques and ASP solvers, or $(ii)$ designing a new ASP solver from scratch. An alternative to these trends is to build on top of state-of-the-art solvers, and to apply machine learning techniques for choosing automatically the "best" available solver on a per-instance basis. In this paper we pursue this latter direction. We first define a set of cheap-to-compute syntactic features that characterize several aspects of ASP programs. Then, we apply classification methods that, given the features of the instances in a {\sl training} set and the solvers' performance on these instances, inductively learn algorithm selection strategies to be applied to a {\sl test} set. We report the results of a number of experiments considering solvers and different training and test sets of instances taken from the ones submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows that, by applying machine learning techniques to ASP solving, it is possible to obtain very robust performance: our approach can solve more instances compared with any solver that entered the 3rd ASP Competition. (To appear in Theory and Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure

Natural language processing and advanced information management

Integrating diverse information sources and application software in a principled and general manner will require a very capable advanced information management (AIM) system. In particular, such a system will need a comprehensive addressing scheme to locate the material in its docuverse. It will also need a natural language processing (NLP) system of great sophistication. It seems that the NLP system must serve three functions. First, it provides an natural language interface (NLI) for the users. Second, it serves as the core component that understands and makes use of the real-world interpretations (RWIs) contained in the docuverse. Third, it enables the reasoning specialists (RSs) to arrive at conclusions that can be transformed into procedures that will satisfy the users' requests. The best candidate for an intelligent agent that can satisfactorily make use of RSs and transform documents (TDs) appears to be an object oriented data base (OODB). OODBs have, apparently, an inherent capacity to use the large numbers of RSs and TDs that will be required by an AIM system and an inherent capacity to use them in an effective way

Analytic Tableaux for Simple Type Theory and its First-Order Fragment

We study simple type theory with primitive equality (STT) and its first-order fragment EFO, which restricts equality and quantification to base types but retains lambda abstraction and higher-order variables. As deductive system we employ a cut-free tableau calculus. We consider completeness, compactness, and existence of countable models. We prove these properties for STT with respect to Henkin models and for EFO with respect to standard models. We also show that the tableau system yields a decision procedure for three EFO fragments

Design and Implementation of a Software System for High Level Business Rules

The Business Rules Group has highlighted the importance of the ownership of business rules by business people. This calls for a business oriented view of business rules. Accordingly, we propose to introduce a Business Layer on top of the CIM layer of business rules that considers the essential nature of business rules, their properties and structure as well as inter-relationships between business rules. We propose a model that inhabits the business layer. This model provides (a) flat and hierarchical business rules, (b) business rules that operate on the state of an enterprise and cause state changes (c) temporal constraints and specification of long running and instantaneous business rules. Further, we develop a Business Rule Management system(BRMS) that, besides basic CRUD capability, allows construction of business rules from given ones. Our proposals are exemplified with a subset of the business rules of a Library