Non-clausal Reasoning with Propositional Definite Theories

  title={Non-clausal Reasoning with Propositional Definite Theories},
  author={Zbigniew Stachniak},
  • Z. Stachniak
  • Published in AISC 16 September 1998
  • Computer Science
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. 
Polarity Guided Tractable Reasoning
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
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
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
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Finding Tractable Formulas in NNF
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
Syntax for Variable Binders: An Overview and Suggestions for Combining Mobile Processes and Declarative Programming.


Completely Non-Clausal Theorem Proving
Completeness for Linear Regular Negation Normal Form Inference Systems
Completeness proofs that generalize the Anderson- Bledsoe excess literal argument are developed for calculi other than resolution, and the completeness of regular, connected tableaux for formulas in negation normal form and NC-resolution under a linear restriction are established.
Connection Based Strategies for Deciding Propositional Temporal Logic
It is shown that a slightly looser generalized subformula property exists for temporal logics, and this property is exploited to develop a temporal notion of polarities and connections, upon which an efficient proof procedure for propositional temporal logic is based.
Resolution proof systems - an algebraic theory
  • Z. Stachniak
  • Computer Science, Chemistry
    Automated reasoning series
  • 1996
This paper presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and expensive process of designing and proving first-Order Resolution Proof Systems.
Model-Theoretic Semantics and Tractable Algorithm for CNF-BCP
A new quadratic-time reasoner, RFP, is presented that infers exactly the same literals as CNF-BCP and is suitable for reasoning with knowledge bases that are built incrementally.
A Machine-Oriented Logic Based on the Resolution Principle
The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.
Foundations of Logic Programming
Many-Valued Logics
The classical logic, intuitionism and the modal logics of Lewis, and fuzzy sets and Zadeh logic, as well as other topics, are examined.
Truth Maintenance
The functionality of truth maintenance systems is discussed and various existing algorithms are compared and applications and directions for future research are discussed.