On Finitely Recursive Programs

Baselice, Sabrina; Bonatti, Piero A.; Criscuolo, Giovanni

doi:10.1007/978-3-540-74610-2_7

Cited by 24 publications

(24 citation statements)

References 14 publications

(26 reference statements)

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“…we can construct the set of attacks on S simply by considering attacks on the members of S in turn. 12 It may be noted that additivity implies that the mapping is also monotonic, i.e. if R ⊆ S then µ(R) ⊆ µ(S).…”

Section: Attack Expressionmentioning

confidence: 99%

Automata for infinite argumentation structures

Baroni

Cerutti

Dunne

et al. 2013

Artificial Intelligence

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The theory of abstract argumentation frameworks (AFs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this limitation, in this paper we propose a novel approach for describing infinite afs using tools from formal language theory. In particular, the possibly infinite set of arguments is specified through the language recognized by a deterministic finite automaton while a suitable formalism, called attack expression, is introduced to describe the relation of attack between arguments.\ud The proposed approach is shown to satisfy some desirable properties which cannot be achieved through other “naive” uses of formal languages. In particular, the approach is shown to be expressive enough to capture (besides any arbitrary finite structure) a large variety of infinite afs including two major examples from previous literature and two sample cases from the domains of multi-agent negotiation and ambient intelligence. On the computational side, we show that several decision and construction problems which are known to be polynomial time solvable in finite afs are decidable in the context of the proposed formalism and we provide the relevant algorithms. Moreover we obtain additional results concerning the case of finitary AFs

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Section: Attack Expressionmentioning

confidence: 99%

Automata for infinite argumentation structures

Baroni

Cerutti

Dunne

et al. 2013

Artificial Intelligence

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“…Since the definitions of the previous section are based on LPADs, and other work in the literature is often based on disjunctive logic programs, we restrict our attention to normal programs, for which the semantics coincide. (Baselice et al 2009) studies the class of finitely recursive programs, which is a superset of finitary programs previously introduced into the literature by the authors. The paper first defines a dependency graph, which for normal programs is essentially the same as Definition 5.…”

Section: Comparisons Of Termination Propertiesmentioning

confidence: 99%

“…Then, there is an SLG evaluation of Q to P using term-depth abstraction that finitely terminates. By the discussion of Section 4.2, Theorem 3 shows that there is an SLG evaluation with term-depth abstraction that will finitely terminate on any ground query to a finitely recursive (Baselice et al 2009) or finitely ground (Calimeri et al 2008) program that is fixed-order dynamically stratified. 6 While SLG itself is ideally complete for all normal programs, the PITA implementation is restricted to fixedorder dynamically stratified programs, so that Theorem 3 is used in the proof of the termination results of Section 8.…”

Section: Theoremmentioning

confidence: 99%

Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

Riguzzi¹,

Swift²

2012

Theory and Practice of Logic Programming

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The distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs) and ProbLog.When a program contains functions symbols, the distribution semantics is well-defined only if the set of explanations for a query is finite and so is each explanation. Welldefinedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper we identify a larger class of programs for which the semantics is well-defined together with an efficient procedure for computing the probability of queries. Since LPADs offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics.We present the algorithm "Probabilistic Inference with Tabling and Answer subsumption" (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

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“…A disjunctive program P is finitely recursive [4,3] iff each ground atom A depends on finitely many ground atoms in DG(P ).…”

Section: Preliminariesmentioning

confidence: 99%

On the decidability of FDNC programs

Bonatti¹

2011

Intelligenza Artificiale

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Il Milione: A Journey in the Computational Logic in Italy 55 SOMMARIO/ABSTRACTQuesto articolo introduce una nuova dimostrazione della decidibilità del controllo di consistenza per i programmi FDNC sotto la semantica dei modelli stabili, basandosi su splitting sequences regolari. Con questa tecnica, riusciamo a rilassare leggermente la definizione di programmi FDNC e muoviamo un primo passo verso l'analisi delle relazioni tra programmi FDNC e la teoria dei programmi finitamente ricorsivi.We provide a new decidability proof for the consistency of FDNC programs under the stable model semantics, based on regular splitting sequences. With this technique, we can slightly relax the definition of FDNC programs and make a first step towards a precise understanding of the relationships between FDNC programs and finitely recursive programs.

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On Finitely Recursive Programs

Cited by 24 publications

References 14 publications

Automata for infinite argumentation structures

Automata for infinite argumentation structures

Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

On the decidability of FDNC programs

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