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## Possibilistic-based argumentation: An answer set programming approach (2008)

Venue: | In Mexican International Conference on Computer Science(ENC |

Citations: | 4 - 0 self |

### Citations

1847 | The stable model semantics for logic programming.
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...rmed formulae) Γ in a logic X . Γ `X S if and only if ∀s ∈ S Γ `X s. 2.2.2 Non-Possibilistic Semantics The answer set semantics was first defined in terms of the so called Gelfond-Lifschitz reduction =-=[22]-=- and it is usually studied in the context of syntax dependent transformations on programs. The following definition of an answer set for general programs generalizes the definition presented in [22] a... |

1774 | Some philosophical problems from the standpoint of artificial intelligence.
- McCarthy, Hayes
- 1969
(Show Context)
Citation Context ..., the commitment to numbers means that any two events must be comparable in terms of their probabilities: either one event is more probable than the other, or they have equal probability. In fact, in =-=[31]-=-, McCarthy and Hayes pointed out that attaching probabilities to a statement has some objections. For instance, The information necessary to assign numerical probabilities is not ordinarily available.... |

1198 | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games.
- Dung
- 1995
(Show Context)
Citation Context ...g because he has fever. Hence, we can say that r2 is the best candidate for transplanting. In order to formalize the managing of conflicts between possibilistic arguments, we will use Dung’s approach =-=[18]-=- for solving the conflicts of a set of possibilistic arguments. Hence, we will define some basic concept that was introduced in [18] in terms of our possibilistic arguments. Definition 9 (Possibilisti... |

1184 |
The Uses of Argument.
- Toulmin
- 2003
(Show Context)
Citation Context ...ns are not available or difficult to get. In fact, by considering partially ordered sets, it is possible to capture the confidence of a claim by using qualifiers like the Toulmin’s famous “qualifiers”=-=[47]-=-. For instance, in [20] Fox and Modgil discuss the expressiveness of these qualifiers for capturing the uncertainty of medical claims. As far as we know, there are few attempts to formalize argument-b... |

1044 | Classical negation in logic programs and disjunctive databases.
- Gelfond, Lifschitz
- 1991
(Show Context)
Citation Context ...ied in the context of syntax dependent transformations on programs. The following definition of an answer set for general programs generalizes the definition presented in [22] and it was presented in =-=[23]-=-: Let P be any extended disjunctive program. For any set S ⊆ LP , let PS be the positive program obtained from P by deleting (i) each rule that has a formula not a in its body with a ∈ S, and then (ii... |

716 | Knowledge Representation, Reasoning and Declarative Problem Solving,
- Baral
- 2003
(Show Context)
Citation Context ... of logic specification languages is a successful approach for encoding knowledge. In the last two decades, one of the most successful logic programming approach has been Answer Set Programming (ASP) =-=[9]-=-. ASP is the realization of much theoretical work on Non-monotonic Reasoning and Artificial Intelligence applications. It represents a new paradigm for logic programming that allows, using the concept... |

446 | Bilattices and the semantics of logic programming.
- FITTING
- 1991
(Show Context)
Citation Context ...ature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., =-=[19, 29]-=-. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion of uncertainty and how uncertainty valu... |

361 |
Reasoning About Uncertainty.
- Halpern
- 2003
(Show Context)
Citation Context ... experience or our commonsense, the question is: how could these statements be captured by real application systems like Multi Agent Systems? For those steeped in probability, Halpern has remarked in =-=[24]-=- that probability has its problems. For one thing, the numbers are not always available. For another, the commitment to numbers means that any two events must be comparable in terms of their probabili... |

277 | Possibilistic logic.
- Dubois, Lang, et al.
- 1994
(Show Context)
Citation Context ...gical agents and Artificial Intelligence [14, 43]. In [34], a possibilistic framework for reasoning under uncertainty was proposed. This framework is a combination between ASP and possibilistic logic =-=[16]-=-. Possibilistic Logic is based on possibilistic theory where at the mathematical level, degrees of possibility and necessity are closely related to fuzzy sets [16]. Thanks to the natural properties of... |

211 | Theory of generalized annotated logic programming and its applications.
- KIFER, SUBRAHMANIAN
- 1992
(Show Context)
Citation Context ...sented a discussion of some of the problems to find a numerical representation for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., =-=[27]-=-. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g... |

160 | V.S.: Probabilistic logic programming.
- Ng, Subrahmanian
- 1992
(Show Context)
Citation Context ...problems to find a numerical representation for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., =-=[33, 30, 26]-=-. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these appr... |

145 | A logic of argumentation for reasoning under uncertainty.
- Krause, Ambler, et al.
- 1995
(Show Context)
Citation Context ...e few attempts to formalize argument-based decision making under uncertainty. Some of the most representative approaches are • Bonet and Geffner approach [11], • works based on Logic of Argumentation =-=[21, 28]-=- and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted [46, 37... |

106 | Quantitative deduction and its fixpoint theory.
- EMDEN
- 1986
(Show Context)
Citation Context ...ion for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., =-=[48, 42, 35]-=-. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion o... |

96 |
Inferring from inconsistency in preference-based argumentation frameworks.
- Amgoud, Cayrol
- 2002
(Show Context)
Citation Context ...= 〈Claim, Support, q〉 be a possibilistic argument w.r.t. P . Then q = GLB{n(r)|r ∈ Support} Proof: The result is direct by Lemma 1. The property of the weakest link has been discussed by some authors =-=[7, 5]-=- as an important property because it could help • to allow an agent to compare different arguments in order to select the best one and • to determine the acceptable arguments among the conflicting one... |

83 | On principle-based evaluation of extension-based argumentation semantics.
- Baroni, Giacomin
- 2007
(Show Context)
Citation Context ...set because Arg1 and Arg2 attack each other. It is worth to comment that conflict-freeness is a simple but important requirement in the selection of sets of arguments. In fact, Baroni and Giocomin in =-=[10]-=- pointed out that conflict-freeness is the minimal requirement in the selection of coherent point of view in a conflict of arguments. • If we consider S = {Arg2, Arg3}, then S is an admissible set. Ob... |

64 |
Evidential support of logic programming
- Baldwin
- 1987
(Show Context)
Citation Context ...d logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., =-=[8]-=-. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion of uncertainty and how uncertainty values, associated to clauses and facts, are managed. T... |

62 | Probabilistic logic programming.
- Lukasiewicz
- 1998
(Show Context)
Citation Context ...problems to find a numerical representation for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., =-=[33, 30, 26]-=-. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these appr... |

56 | Arguing for decisions: A qualitative model of decision making.
- Bonet, Geffner
- 1996
(Show Context)
Citation Context ...of medical claims. As far as we know, there are few attempts to formalize argument-based decision making under uncertainty. Some of the most representative approaches are • Bonet and Geffner approach =-=[11]-=-, • works based on Logic of Argumentation [21, 28] and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human org... |

48 |
Towards possibilistic logic programming.
- Dubois, Lang, et al.
- 1991
(Show Context)
Citation Context ... probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., =-=[15, 4, 3, 2, 34]-=-. Basically, these approaches differ in the underlying notion of uncertainty and how uncertainty values, associated to clauses and facts, are managed. To prioritize logic clauses, as it is done in our... |

30 | Possibilistic logic: a retrospective and prospective view.
- Dubois, Prade
- 2004
(Show Context)
Citation Context ... answer set programming. Possibilistic logic has a basic principle that: The strength of a conclusion is the strength of the weakest argument used in its proof. In fact, according to Dubois and Prade =-=[17]-=-, the contribution of possibilistic logic setting is to relate this principle (measuring the validity of an inference chain by its weakest link) to fuzzy set-based necessity measures in the framework ... |

28 |
Godo,A complete calculus for possibilistic logic programming with fuzzy propositional variables
- Alsinet, L
(Show Context)
Citation Context ...ic programming approach presented in [39, 38, 40, 36], we are not only able to manage conflict information but also we are able to restore inconsistent knowledge based. It is worth to comment that in =-=[3]-=-, a possibilistic logic programming approach is defined over the many-valued Gödel logic. The syntax of this approach is restricted to a Horn-clause sublanguage of the many-valued Gödel logic; hence... |

26 |
Using arguments for making decisions: A possibilistic logic approach
- Amgoud, Prade
(Show Context)
Citation Context ...ertainty. Some of the most representative approaches are • Bonet and Geffner approach [11], • works based on Logic of Argumentation [21, 28] and • more recently works based on the Possibilistic Logic =-=[6, 1, 2]-=-. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted [46, 37, 45]. Our experience suggests that in our medical domain, we require... |

26 |
Possibilistic Uncertainty Handling for Answer Set Programming.
- Nicolas, Garcia, et al.
- 2006
(Show Context)
Citation Context ...monotonic reasoning. The efficiency of the answer set solvers have allowed to increase the list of ASP’s practical applications e.g., planning, logical agents and Artificial Intelligence [14, 43]. In =-=[34]-=-, a possibilistic framework for reasoning under uncertainty was proposed. This framework is a combination between ASP and possibilistic logic [16]. Possibilistic Logic is based on possibilistic theory... |

21 | T.: Combining probabilistic logic programming with the power of maximum entropy
- Kern-Isberner, Lukasiewicz
- 2004
(Show Context)
Citation Context ...problems to find a numerical representation for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., =-=[33, 30, 26]-=-. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these appr... |

19 | An epistemic foundation for logic programming with uncertainty
- Lakshmanan
- 1994
(Show Context)
Citation Context ...ature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., =-=[19, 29]-=-. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion of uncertainty and how uncertainty valu... |

17 | Semantics for possibilistic disjunctive programs.
- Nieves, Osorio, et al.
- 2007
(Show Context)
Citation Context ...d uncertain. Nicolas et al.’s approach is based on the concept of possibilistic stable model which defines a semantics for possibilistic normal logic programs. Following Nicolas et al.’s approach, in =-=[39, 38, 40]-=-, an possibilistic disjunctive logic programming approach was introduced. This approach is able to deal with reasoning under uncertainty and incomplete information. It permits to use explicit labels l... |

16 | A logic programming framework for possibilistic argumentation: Formalization and logical properties. Fuzzy Sets and Systems,
- Alsinet, Chesnevar, et al.
- 2008
(Show Context)
Citation Context ...ertainty. Some of the most representative approaches are • Bonet and Geffner approach [11], • works based on Logic of Argumentation [21, 28] and • more recently works based on the Possibilistic Logic =-=[6, 1, 2]-=-. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted [46, 37, 45]. Our experience suggests that in our medical domain, we require... |

14 |
Judgment under uncertainty:heuristics and biases.
- Kahneman, Slovic, et al.
- 1982
(Show Context)
Citation Context ... This gives rise to “biases” in judgments concerning what they “really” want to do. A deep study of the importance of the biasses and heuristics in judgment under uncertainty is presented in the book =-=[25]-=-. In view of the fact that we know that a reasoning based on arguments which are quantified by relative likelihoods could capture our experience or our commonsense, the question is: how could these st... |

12 |
L.: Towards an automated deduction system for first-order possibilistic logic programming with fuzzy constants
- Alsinet, Godo
- 2002
(Show Context)
Citation Context ... probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., [48, 42, 35]. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., =-=[15, 4, 3, 2, 34]-=-. Basically, these approaches differ in the underlying notion of uncertainty and how uncertainty values, associated to clauses and facts, are managed. To prioritize logic clauses, as it is done in our... |

11 |
Introduction to Mathematical Logic. Chapman and Hall, fourth edn.
- Mendelson
- 1997
(Show Context)
Citation Context .... We assume familiarity with basic concepts in classic logic and in the semantics of logic programs e.g., interpretations, models, etc. A good introductory treatment of these concepts can be found in =-=[9, 32]-=-. 2.1 Possibilistic Logic A necessity-valued formula is a pair (ϕ α) where ϕ is a classical logic formula and α ∈ (0, 1] is a positive number. The pair (ϕ α) expresses that the formula ϕ is certain at... |

11 | Using arguing agents to increase the human organ pool for transplantation
- Tolchinsky, Cortes, et al.
- 2005
(Show Context)
Citation Context ...21, 28] and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted =-=[46, 37, 45]-=-. Our experience suggests that in our medical domain, we require a qualitative theory of default reasoning for modeling incomplete information and a quantitative theory like possibilistic logic for mo... |

10 | Formalizing argumentative reasoning in a possibilistic logic programming setting with fuzzy unification.
- Alsinet, Chesnevar, et al.
- 2008
(Show Context)
Citation Context ...ertainty. Some of the most representative approaches are • Bonet and Geffner approach [11], • works based on Logic of Argumentation [21, 28] and • more recently works based on the Possibilistic Logic =-=[6, 1, 2]-=-. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted [46, 37, 45]. Our experience suggests that in our medical domain, we require... |

9 | Quantitative logic programming revisited.
- Rodrıguez-Artalejo, Romero-Dıaz
- 2008
(Show Context)
Citation Context ...ion for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., =-=[48, 42, 35]-=-. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion o... |

8 |
Modelling Argumentation with Belief Networks.
- Carofiglio
- 2004
(Show Context)
Citation Context ... For another, the commitment to numbers means that any two events must be comparable in terms of probability: either one event is more probable than the other, or they have equal probability [24]. In =-=[13]-=-, it was proposed an interesting argumentation approach where the degree of belief in the argument’s conclusion depends on the degree of belief in the argument’s premises. This approach is so useful w... |

8 | Pstable semantics for possibilistic logic programs.
- Osorio, Nieves
- 2007
(Show Context)
Citation Context ...d uncertain. Nicolas et al.’s approach is based on the concept of possibilistic stable model which defines a semantics for possibilistic normal logic programs. Following Nicolas et al.’s approach, in =-=[39, 38, 40]-=-, an possibilistic disjunctive logic programming approach was introduced. This approach is able to deal with reasoning under uncertainty and incomplete information. It permits to use explicit labels l... |

8 | 2006c, Increasing Human-Organ Transplant Availability: Argumentation-Based Agent Deliberation
- Tolchinsky, Cortés, et al.
(Show Context)
Citation Context ...21, 28] and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted =-=[46, 37, 45]-=-. Our experience suggests that in our medical domain, we require a qualitative theory of default reasoning for modeling incomplete information and a quantitative theory like possibilistic logic for mo... |

6 | Answer sets: From constraint programming towards qualitative optimization
- Brewka
(Show Context)
Citation Context ...y degrees as preferences, it was defined a preference relations between arguments (Definition 7). The use of qualitative preferences in logic programming has been suggested by authors as G. Brewka in =-=[12]-=-. The Brewka’s approach is also motivated from the fact that a variety of applications numerical information is hard to obtain. To have a correct understanding of the relationship between Brewka’s app... |

5 |
An introduction to fuzzy answer set programming
- Nieuwenborgh, Cock, et al.
- 2007
(Show Context)
Citation Context ...ion for uncertainty. proaches in the literature employ one of the following formalisms: • annotated logic programming, e.g., [27]. • probabilistic logic, e.g., [33, 30, 26]. • fuzzy set theory, e.g., =-=[48, 42, 35]-=-. • multi-valued logic, e.g., [19, 29]. • evidence theoretic logic programming, e.g., [8]. • possibilistic logic, e.g., [15, 4, 3, 2, 34]. Basically, these approaches differ in the underlying notion o... |

5 |
Modeling arguments and uncertain information — A non-monotonic reasoning approach
- Nieves
- 2008
(Show Context)
Citation Context ...an the inconsistent degree of the inconsistent knowledge base. By considering this idea, the authors of [34] defined the concept of α-cut for possibilistic logic programs. This idea also was taken in =-=[36]-=- in order to restore consistency in any inconsistent possibilistic program, in the context of the possibilistic answer set and pstable semantics. For instance by applying α-cut to Pinc, we can reduce ... |

3 |
From arguments to decisions: Extending the Toulmin view
- FOX, MODGIL
(Show Context)
Citation Context ... difficult to get. In fact, by considering partially ordered sets, it is possible to capture the confidence of a claim by using qualifiers like the Toulmin’s famous “qualifiers”[47]. For instance, in =-=[20]-=- Fox and Modgil discuss the expressiveness of these qualifiers for capturing the uncertainty of medical claims. As far as we know, there are few attempts to formalize argument-based decision making un... |

3 |
Applications of Uncertainty Formalisms, chapter Arguing about beliefs and actions
- Fox, Parsons
- 1998
(Show Context)
Citation Context ...e few attempts to formalize argument-based decision making under uncertainty. Some of the most representative approaches are • Bonet and Geffner approach [11], • works based on Logic of Argumentation =-=[21, 28]-=- and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted [46, 37... |

3 |
Scope of Logic, Methodology and Philosophy
- Pelletier, Elio
- 2002
(Show Context)
Citation Context ...t a reasoning based on these kinds of statements could reach biased conclusions. However, these conclusions could reflect the experience or commonsense of an expert. Pelletier and Elio pointed out in =-=[41]-=- that people simply have tendencies to ignore certain information because of the (evolutionary) necessity to make decisions quickly. This gives rise to “biases” in judgments concerning what they “real... |

2 |
Supporting decision making in organ transplating using argumentation theory
- Nieves, Osorio, et al.
- 2006
(Show Context)
Citation Context ...21, 28] and • more recently works based on the Possibilistic Logic [6, 1, 2]. We have been working in the decision making process for deciding if a human organ is viable or not for being transplanted =-=[46, 37, 45]-=-. Our experience suggests that in our medical domain, we require a qualitative theory of default reasoning for modeling incomplete information and a quantitative theory like possibilistic logic for mo... |

1 |
Deliverable D2.1: Theoretical framework for argumentation. Argumentation Service Plarform with Integrated Components
- Project
- 2004
(Show Context)
Citation Context ...= 〈Claim, Support, q〉 be a possibilistic argument w.r.t. P . Then q = GLB{n(r)|r ∈ Support} Proof: The result is direct by Lemma 1. The property of the weakest link has been discussed by some authors =-=[7, 5]-=- as an important property because it could help • to allow an agent to compare different arguments in order to select the best one and • to determine the acceptable arguments among the conflicting one... |

1 |
Uncertainty in logic programming. Association for Logic Programming
- Subrahmanian
- 2007
(Show Context)
Citation Context ... research area. In fact, it has proceeded along various research lines of logic logic programming. An interesting historical recollection in this topic was recently presented by V. S. Subrahmanian in =-=[44]-=-. In this recollection he highlights some phases in the evolution of the topic from the viewpoint of a committed researcher. Research on logic programming with uncertainty has dealt with various appro... |