MACE 2.0 Reference Manual and Guide

MACE is a program that searches for finite models of first-order statements. The statement to be modeled is first translated to clauses, then to relational clauses; finally for the given domain size, the ground instances are constructed. A Davis-Putnam-Loveland-Logeman procedure decides the propositional problem, and any models found are translated to first-order models. MACE is a useful complement to the theorem prover Otter, with Otter searching for proofs and MACE looking for countermodels.Comment: 10 page

Super Logic Programs

The Autoepistemic Logic of Knowledge and Belief (AELB) is a powerful nonmonotic formalism introduced by Teodor Przymusinski in 1994. In this paper, we specialize it to a class of theories called `super logic programs'. We argue that these programs form a natural generalization of standard logic programs. In particular, they allow disjunctions and default negation of arbibrary positive objective formulas. Our main results are two new and powerful characterizations of the static semant ics of these programs, one syntactic, and one model-theoretic. The syntactic fixed point characterization is much simpler than the fixed point construction of the static semantics for arbitrary AELB theories. The model-theoretic characterization via Kripke models allows one to construct finite representations of the inherently infinite static expansions. Both characterizations can be used as the basis of algorithms for query answering under the static semantics. We describe a query-answering interpreter for super programs which we developed based on the model-theoretic characterization and which is available on the web.Comment: 47 pages, revised version of the paper submitted 10/200

Computing Preferred Answer Sets by Meta-Interpretation in Answer Set Programming

Most recently, Answer Set Programming (ASP) is attracting interest as a new paradigm for problem solving. An important aspect which needs to be supported is the handling of preferences between rules, for which several approaches have been presented. In this paper, we consider the problem of implementing preference handling approaches by means of meta-interpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable meta-interpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a meta-interpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced meta-interpreters, which make use of graph-based characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledge-representation formalisms.Comment: 34 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports

Implementing Default and Autoepistemic Logics via the Logic of GK

The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), autoepistemic logic, Turner's logic of universal causation, and general logic programming under stable model semantics. Besides showing the generality of GK as a logic for nonmonotonic reasoning, these embeddings shed light on the relationships among these other logics. In this paper, for the first time, we show how the logic of GK can be embedded into disjunctive logic programming in a polynomial but non-modular translation with new variables. The result can then be used to compute the extension/expansion semantics of default logic, autoepistemic logic and Turner's logic of universal causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity

We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV^K system, which implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna University of Technology, see http://www.kr.tuwien.ac.at/research/reports