Query Answering in Normal Logic Programs Under Uncertainty

Straccia, Umberto

doi:10.1007/11518655_58

Cited by 25 publications

(41 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We then have that I is the minimal fuzzy model of P iff I is the minimal fuzzy model ofP 2 iff I is the least solution of a = max(min(b + 3, 12), 6, 0) b = max(min(a, 4), 0) with I(a) = I (a) 12 and I(b) = I (b) 12 . However, as we will show in the following subsections, for several subclasses of regular simple (and definite) FASP programs, we can show Pmembership, even if the constants in the program are not polynomially bounded.…”

Section: Complexity Of Regular Definite Fasp Programsmentioning

confidence: 99%

See 1 more Smart Citation

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Blondeel

Schockaert

Vermeir

et al. 2014

International Journal of Approximate Reasoning

View full text Add to dashboard Cite

Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Lukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules -a syntactic generalization which does not affect the expressivity of ASP in the classical case -the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully

show abstract

Section: Complexity Of Regular Definite Fasp Programsmentioning

confidence: 99%

“…[8,9,10,11,12,13,14]). The main differences are the type of connectives that are allowed, the truth lattices that are used, the definition of a model of a program and the way that partial satisfaction of rules is handled.…”

Section: Introductionmentioning

confidence: 99%

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Blondeel

Schockaert

Vermeir

et al. 2014

International Journal of Approximate Reasoning

View full text Add to dashboard Cite

show abstract

“…The AWA has many applications (see [16]), among which: (i) Extended Logic Programs (ELPs) (e.g., [2,3,12]); (ii) many-valued logic programming with non-monotone negation (e.g., [5,23]); (iii) paraconsistency (e.g., [1,3,4]) and (iv)representation of default rules by relying on the so-called abnormality theory [19].…”

Section: Introductionmentioning

confidence: 99%

A Top-Down Query Answering Procedure for Normal Logic Programs Under the Any-World Assumption

Straccia

2007

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. The Any-World Assumption (AWA) has been introduced for normal logic programs as a generalization of the well-known notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows any assignment (i.e., interpretation), over a truth space (bilattice), to be a default assumption and, thus, the CWA and OWA are just special cases. To answer queries, we provide a novel and simple top-down procedure.

show abstract

“…From computational point of view, by a similar analysis as in [9], it can be shown that T opAnswer is exponential with respect to |P| (combined complexity), but polynomial in |P E | (data complexity), and we have:…”

Section: T Opanswersmentioning

confidence: 89%

“…, x n ) ≤ x i . In this case it can be shown that the least-fixed point is reached after a finite number of T p iterations [9].…”

Section: Preliminariesmentioning

confidence: 99%

Towards Vague Query Answering in Logic Programming for Logic-Based Information Retrieval

Straccia

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We address a novel issue for logic programming, namely the problem of evaluating ranked top-k queries. The problem occurs for instance, when we allow queries such as "find cheap hotels close to the conference location" in which vague predicates like cheap and close occur. Vague predicates have the effect that each tuple in the answer set has now a score in [0,1]. We show how to compute the top-k answers in case the set of facts is huge, without evaluating all the tuples.

show abstract

Query Answering in Normal Logic Programs Under Uncertainty

Cited by 25 publications

References 17 publications

Complexity of fuzzy answer set programming under Łukasiewicz semantics

Complexity of fuzzy answer set programming under Łukasiewicz semantics

A Top-Down Query Answering Procedure for Normal Logic Programs Under the Any-World Assumption

Towards Vague Query Answering in Logic Programming for Logic-Based Information Retrieval

Contact Info

Product

Resources

About