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Non-clausal reasoning with propositional definite theories [chapter]

Zbigniew Stachniak
1998 Lecture Notes in 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.  ...  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  ...  We begin with the formal definition of a definite formula.  ... 
doi:10.1007/bfb0055921 fatcat:onfhgujs2rcpffkwtpgmhe5k2m

Equivalence of Logic Programs Under Updates [chapter]

Katsumi Inoue, Chiaki Sakama
2004 Lecture Notes in Computer Science  
. † These equivalence relations compare capabilities of deductive reasoning between programs.  ...  4 Comparing non-deductive capabilities between programs Intelligent agents perform non-deductive commonsense reasoning as well as deductive reasoning.  ...  Corollary: Deciding inductive equivalence of two propositional clausal theories is coNP-complete.  ... 
doi:10.1007/978-3-540-30227-8_17 fatcat:jnclh6ctkjbfbgpkbdflkzbzci

Inductive Equivalence of Logic Programs [chapter]

Chiaki Sakama, Katsumi Inoue
2005 Lecture Notes in Computer Science  
. † These equivalence relations compare capabilities of deductive reasoning between programs.  ...  4 Comparing non-deductive capabilities between programs Intelligent agents perform non-deductive commonsense reasoning as well as deductive reasoning.  ...  Corollary: Deciding inductive equivalence of two propositional clausal theories is coNP-complete.  ... 
doi:10.1007/11536314_19 fatcat:ytly42423rd5hbxn2wzr4x5n74

Normal forms for inductive logic programming [chapter]

Peter A. Flach
1997 Lecture Notes in Computer Science  
In this paper we study induction of unrestricted clausal theories from interpretations.  ...  First, we show that in the propositional case induction from complete evidence can be seen as an equivalence-preserving transformation from DNF to CNF.  ...  Khardon & Roth (1994) investigate efficient reasoning with models rather than theories.  ... 
doi:10.1007/3540635149_43 fatcat:57kpgrgsnfhxxaaiq7sdx5y3r4

The Horn Non-Clausal Class and its Polynomiality [article]

Gonzalo E. Imaz
2021 arXiv   pre-print
The expressiveness of propositional non-clausal (NC) formulas is exponentially richer than that of clausal formulas. Yet, clausal efficiency outperforms non-clausal one.  ...  Indeed, a major weakness of the latter is that, while Horn clausal formulas, along with Horn algorithms, are crucial for the high efficiency of clausal reasoning, no Horn-like formulas in non-clausal form  ...  adapted to different reasoning problems; and (ii) our work can be used as a lever to develop the NC paradigm; for example, our definition of UR nc is the basis to conceive a new definition of Non-Clausal  ... 
arXiv:2108.13744v3 fatcat:5vpb3cmqxbgs7hviclkovvltqq

A First Polynomial Non-Clausal Class in Many-Valued Logic [article]

Gonzalo E. Imaz
2021 arXiv   pre-print
As a consequence, a first polynomial propositional class in non-clausal (NC) form has recently been proposed.  ...  DPLL-based approximate reasoning.  ...  In many frameworks of non-classical and classical logics, non-clausal formulas are often translated into clausal form e.g. [58, 12, 30] to which clausal reasoning methods are then applied.  ... 
arXiv:2110.12901v1 fatcat:xgh5xriufvampbfxh5hsoyls3i

Logical settings for concept-learning

Luc De Raedt
1997 Artificial Intelligence  
The implications of this result for inductive logic programming and computational learning theory are then discussed, and guidelines for choosing a problem-setting are formulated. @ 1997 Elsevier Science  ...  Some of the reductions will represent Herbrand interpretations by clausal theories as follows: 3 Definition 10.  ...  Hence, partial interpretations can represent examples with missing values. When learning from clausal theories, M(e) can (depending on the example) contain any set of Herbrand interpretations.  ... 
doi:10.1016/s0004-3702(97)00041-6 fatcat:eod5fx34sve4tohdnwqq3abztm

Non-Clausal Multi-ary a-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

Yang Xu, Jun Liu, Xingxing He, Xiaomei Zhong, Shuwei Chen
2018 International Journal of Computational Intelligence Systems  
is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form.  ...  The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure -lattice implication algebras  ...  The definitions of the general form of non-clausal multi-ary α-generalized resolution and non-clausal multi-ary α-generalized resolution deduction in LP(X) were given, along with its soundness and completeness  ... 
doi:10.2991/ijcis.11.1.29 fatcat:7x6aid2wxjgedox57jy74az5sq

Characterizing and extending answer set semantics using possibility theory

KIM BAUTERS, STEVEN SCHOCKAERT, MARTINE DE COCK, DIRK VERMEIR
2014 Theory and Practice of Logic Programming  
In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.  ...  In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold.  ...  Proposition 13 (weak disjunction, positive clausal program; brave reasoning) Let P be a positive clausal program.  ... 
doi:10.1017/s147106841300063x fatcat:qi6sp2bwgveqzopi7ovxzagr7q

Model-Baded Abduction via Dual Resolution

Fernando Soler-Toscano, Ángel Nepomuceno-Fernández, Atocha Aliseda-Llera
2006 Logic Journal of the IGPL  
Introduction Abductive reasoning is present in many disciplines, in which a way for reasoning with incomplete information is at call.  ...  Given a theory Θ 1 ⊂ L p , and an observation φ ∈ L p , such that Θ 1 , φ is an abductive problem (definition 2.1), we represent by Abd(Θ 1 , φ) the (non-empty) set of abductive solutions (definition 2.2  ...  We find the following reasons for such a claim:  ... 
doi:10.1093/jigpal/jzk020 fatcat:mgvltdeejbbufnvyqm35ymv62i

Actual Causality in a Logical Setting

Alexander Bochman
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
We compare our definition with other, mainly counterfactual, approaches on standard examples.  ...  We provide a definition of actual causation in the logical framework of the causal calculus, which is based on a causal version of the well-known NESS (or INUS) condition.  ...  Definition 8 (actual cause). Let α be a causal world of a parsimonious clausal causal theory ∆.  ... 
doi:10.24963/ijcai.2018/239 dblp:conf/ijcai/Bochman18 fatcat:kscnyo2unbdhhgxkokcwuosnha

Inductive equivalence in clausal logic and nonmonotonic logic programming

Chiaki Sakama, Katsumi Inoue
2010 Machine Learning  
In this paper, we consider clausal logic and nonmonotonic logic programs as representation languages for background theories.  ...  A background theory is called inductively equivalent to another background theory if the two theories induce the same hypotheses for any observation.  ...  Proposition 3.9 (Complexity for deciding inductive equivalence between clausal theories) Deciding inductive equivalence of two propositional clausal theories is coNP-complete under both the classical semantics  ... 
doi:10.1007/s10994-010-5189-4 fatcat:vxaidrnzg5brle4rxdazclg4pu

Weak and Strong Disjunction in Possibilistic ASP [chapter]

Kim Bauters, Steven Schockaert, Martine De Cock, Dirk Vermeir
2011 Lecture Notes in Computer Science  
The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework.  ...  Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules.  ...  Possibilistic logic (PL) [7] , which is based on possibility theory [17] , allows us to reason about (partial) ignorance or uncertainty in a non-probabilistic way.  ... 
doi:10.1007/978-3-642-23963-2_37 fatcat:jrscnavmqzbu7lcbec3nhuo26q

Brave induction: a logical framework for learning from incomplete information

Chiaki Sakama, Katsumi Inoue
2009 Machine Learning  
We analyze computational complexity of decision problems for induction on propositional theories.  ...  We first investigate formal properties of brave induction, then develop an algorithm for computing hypotheses in full clausal theories.  ...  Brave induction can induce non-Horn clauses from a full clausal theory with incomplete observations.  ... 
doi:10.1007/s10994-009-5113-y fatcat:z36rccdhjjbczctzqneq2rwwxy

A Principle for Incorporating Axioms into the First-Order Translation of Modal Formulae [chapter]

Renate A. Schmidt, Ullrich Hustadt
2003 Lecture Notes in Computer Science  
In this paper we present a translation principle, called the axiomatic translation, for reducing propositional modal logics with background theories, including triangular properties such as transitivity  ...  Soundness is automatic under reasonable assumptions, and termination of ordered resolution is easily achieved, but the non-trivial part of the approach is proving completeness.  ...  Definitional clausal forms.  ... 
doi:10.1007/978-3-540-45085-6_36 fatcat:l4qebca3gba4xpz3exmdfzg3i4
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