Termination Proofs for Logic Programs with Tabling

Tabled logic programming is receiving increasing attention in the Logic Programming community. It avoids many of the shortcomings of SLD execution and provides a more flexible and often extremely efficient execution mechanism for logic programs. In particular, tabled execution of logic programs terminates more often than execution based on SLD-resolution. In this article, we introduce two notions of universal termination of logic programming with Tabling: quasi-termination and (the stronger notion of) LG-termination. We present sufficient conditions for these two notions of termination, namely quasi-acceptability and LG-acceptability, and we show that these conditions are also necessary in case the tabling is well-chosen. Starting from these conditions, we give modular termination proofs, i.e., proofs capable of combining termination proofs of separate programs to obtain termination proofs of combined programs. Finally, in the presence of mode information, we state sufficient conditions which form the basis for automatically proving termination in a constraint-based way.Comment: 48 pages, 6 figures, submitted to ACM Transactions on Computational Logic (TOCL

GEM: a Distributed Goal Evaluation Algorithm for Trust Management

Trust management is an approach to access control in distributed systems where access decisions are based on policy statements issued by multiple principals and stored in a distributed manner. In trust management, the policy statements of a principal can refer to other principals' statements; thus, the process of evaluating an access request (i.e., a goal) consists of finding a "chain" of policy statements that allows the access to the requested resource. Most existing goal evaluation algorithms for trust management either rely on a centralized evaluation strategy, which consists of collecting all the relevant policy statements in a single location (and therefore they do not guarantee the confidentiality of intensional policies), or do not detect the termination of the computation (i.e., when all the answers of a goal are computed). In this paper we present GEM, a distributed goal evaluation algorithm for trust management systems that relies on function-free logic programming for the specification of policy statements. GEM detects termination in a completely distributed way without disclosing intensional policies, thereby preserving their confidentiality. We demonstrate that the algorithm terminates and is sound and complete with respect to the standard semantics for logic programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Relational Programming in miniKanren: Techniques, Applications, and Implementations

Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009The promise of logic programming is that programs can be written relationally, without distinguishing between input and output arguments. Relational programs are remarkably flexible—for example, a relational type-inferencer also performs type checking and type inhabitation, while a relational theorem prover generates theorems as well as proofs and can even be used as a simple proof assistant. Unfortunately, writing relational programs is difficult, and requires many interesting and unusual tools and techniques. For example, a relational interpreter for a subset of Scheme might use nominal unification to support variable binding and scope, Constraint Logic Programming over Finite Domains (CLP(FD)) to implement relational arithmetic, and tabling to improve termination behavior. In this dissertation I present miniKanren, a family of languages specifically designed for relational programming, and which supports a variety of relational idioms and techniques. I show how miniKanren can be used to write interesting relational programs, including an extremely flexible lean tableau theorem prover and a novel constraint-free binary arithmetic system with strong termination guarantees. I also present interesting and practical techniques used to implement miniKanren, including a nominal unifier that uses triangular rather than idempotent substitutions and a novel “walk”-based algorithm for variable lookup in triangular substitutions. The result of this research is a family of languages that supports a variety of relational idioms and techniques, making it feasible and useful to write interesting programs as relations

Abduction in Well-Founded Semantics and Generalized Stable Models

Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that provides a level of declarativity superior to that of Prolog, and which has supported successful applications in fields such as parsing, program analysis, and model checking. In this paper we show how to use tabled logic programming to evaluate queries to abductive frameworks with integrity constraints when these frameworks contain both default and explicit negation. The result is the ability to compute abduction over well-founded semantics with explicit negation and answer sets. Our approach consists of a transformation and an evaluation method. The transformation adjoins to each objective literal $O$ in a program, an objective literal $not(O)$ along with rules that ensure that $not(O)$ will be true if and only if $O$ is false. We call the resulting program a {\em dual} program. The evaluation method, \wfsmeth, then operates on the dual program. \wfsmeth{} is sound and complete for evaluating queries to abductive frameworks whose entailment method is based on either the well-founded semantics with explicit negation, or on answer sets. Further, \wfsmeth{} is asymptotically as efficient as any known method for either class of problems. In addition, when abduction is not desired, \wfsmeth{} operating on a dual program provides a novel tabling method for evaluating queries to ground extended programs whose complexity and termination properties are similar to those of the best tabling methods for the well-founded semantics. A publicly available meta-interpreter has been developed for \wfsmeth{} using the XSB system.Comment: 48 pages; To appear in Theory and Practice in Logic Programmin