# Non-clausal Reasoning with Propositional Definite Theories

@inproceedings{Stachniak1998NonclausalRW, title={Non-clausal Reasoning with Propositional Definite Theories}, author={Zbigniew Stachniak}, booktitle={AISC}, year={1998} }

In this paper we propose a non-clausal representational formalism (of definite formulas) that retains the syntactic flavor and algorithmic advantages of Horn clauses. The notion of a definite formula is generic in the sense that it is available to any logical calculus. We argue that efficient automated reasoning techniques which utilize definite formula representation of knowledge (such as SLD-resolution) can be developed for classical and a variety of non-classical logics.

## 6 Citations

Polarity Guided Tractable Reasoning

- Computer ScienceAAAI/IAAI
- 1999

P-BCP is a sound, incomplete, and linear-time inference procedure for classical logic that can be adopted for tractable reasoning in a number of non-classical logics (including some modal and finitely-valued logics).

An Efficient Proof Method for Non-clausal Reasoning

- Computer ScienceISMIS
- 2000

It is proved that some non-clausal Hornlike formulas can be solved in linear time and a correct refutational calculi is provided.

Extending Polynomiality to a Class of Non-clausal Many-Valued Horn-Like Formulas

- Computer ScienceECSQARU
- 2001

It is shown that certain nonclausal many-valued SAT problems can be solved in polynomial time too, extending in this way, earlier results from the clausal framework to the more general non-Clausal one.

TR-2003-09 The HORN-NNF-SAT problem is linear

- Computer Science
- 2003

This paper defines non-clausal formulas that codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols and establishes a sound and refutation complete logical calculus.

Finding Tractable Formulas in NNF

- Computer ScienceComputational Logic
- 2000

This paper defines three non normal Horn-like classes of formulas and defines sound and refutational complete inference rule sets for each class, and designs a sound, complete and strictly linear running time algorithm for eachclass.

Computational Logic — CL 2000

- Computer ScienceLecture Notes in Computer Science
- 2000

Syntax for Variable Binders: An Overview and Suggestions for Combining Mobile Processes and Declarative Programming.

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