Marcelo Finger - Academia.edu (original) (raw)

Papers by Marcelo Finger

Argumentation can be modelled at an abstract level using an argument graph (i.e. a directed graph... more Argumentation can be modelled at an abstract level using an argument graph (i.e. a directed graph where each node denotes an argument and each arc denotes an attack by one argument on another). Since argumentation involves uncertainty, it is potentially valuable to consider how this can quantified in argument graphs. In this talk, we will consider two probabilistic approaches for modeling uncertainty in argumentation. The first is the structural approach which involves a probability distribution over the subgraphs of the argument graph, and this can be used to represent the uncertainty over the structure of the graph. The second is the epistemic approach which involves a probability distribution over the subsets of the arguments, and this can be used to represent the uncertainty over which arguments are believed. The epistemic approach can be constrained to be consistent with Dungs dialectical semantics, but it can also be used as a potential valuable alternative to Dungs dialectica...

Contradictions, from Consistency to Inconsistency, 2018

In this paper we show several similarities among logic systems that deal simultaneously with dedu... more In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous properties hold throughout that class, for whose members there exists a set of linear algebraic techniques applicable in the study of satisfiability decision problems. In this presentation, we consider as Quantitative Logic Reasoning the tasks performed by propositional Probabilistic Logic; first-order logic with counting quantifiers over a fragment containing unary and limited binary predicates; and propositional Lukasiewicz Infinitely-valued Probabilistic Logic. Boole (1854, Chapter XVI, 4, p.189) Deciding if a given set of probabilities is consistent or coherent may be seen as a first step for Boole's "probability extension problem". Indeed, there is certainly more than one way of computing probabilities starting from the establishment of their coherence; see (de Finetti 2017) and also the methods presented in this work. For the purposes of this work, we concentrate on the decision problem of probabilistic logic, the Probabilistic Satisfiability problem (PSAT), which consists of an assignment of probabilities to a set of propositional formulas, and its solution consists of a decision on whether this assignment is satisfiable; this formulation is based on a full Boolean Algebra which, due to de Finetti's Dutch Book Theorem (see Proposition 2.5 below), is equivalent to deciding the coherence criterion over a finite Boolean Algebra. The problem has been first proposed by Boole and has since been independently rediscovered several times (see (Hailperin 1986; Hansen and Jaumard 2000) for a historical account) until it was presented to the Computer Science and Artificial Intelligence community by Nilsson (Nilsson 1986) and was shown to be an NP-complete problem, even for cases where the corresponding classical satisfiability is known to be in PTIME (Georgakopoulos, Kavvadias, and Papadimitriou 1988). Boole's original formulation of the PSAT problem did not consider conditional probabilities, but extensions for them have been developed (Hailperin 1986;

Nesta tese apresentamos o projeto e a implementação do KEMS, um provador de teoremas multi-estrat... more Nesta tese apresentamos o projeto e a implementação do KEMS, um provador de teoremas multi-estratégia baseado no método de tablôs KE. Um provador de teoremas multi-estratégiaé um provador de teoremas onde podemos variar as estratégias utilizadas sem modificar o núcleo da implementação. Além de multi-estratégia, KEMSé capaz de provar teoremas em três sistemas lógicos: lógica clássica proposicional, mbC e mCi. Listamos abaixo algumas das contribuições deste trabalho: A Deus, por tudo. Agradecimentos Ao professor Marcelo Finger, que me orientou, apoiou e encorajou durante todo este processo. Aos professores Walter Carnielli, Marcelo Coniglio eÍtala D'Ottaviano, que tão bem me acolheram no CLE-Unicamp. Em particular ao Walter pelas críticas e sugestões feitas a tese e ao Coniglio pelos comentários feitos durante o desenvolvimento do trabalho. A professora Renata Wassermann, pelas críticas e sugestões feitasà tese e durante o desenvolvimento do trabalho. Aos professores Mario Benevides e Guilherme Bittencourt, pelas críticas e sugestões feitasà tese. A todos os professores da pós-graduação de Departamento de Ciência da Computação do IME-USP, em especial a Flávio Soares, Fabio Kon, Carlos Eduardo Ferreira e Leliane Nunes. Também ao professor Jacques Wainer, do IC-Unicamp. Aos que me estimularam e me ajudaram a iniciar o doutorado: Evandro Costa, Guilherme Ataíde, Valdemar Setzer, Liliane, Luiz Elias, Ruy de Queiroz e os amigos e excolegas de trabalho do CEFET-AL. Aos colegas (do CLE, IME, IC-Unicamp e de outros ambientes por onde circulei nestes anos

Journal of the Brazilian Computer Society, 2015

Background: This paper studies the generalized probabilistic satisfiability (GPSAT) problem, wher... more Background: This paper studies the generalized probabilistic satisfiability (GPSAT) problem, where the probabilistic satisfiability (PSAT) problem is extended by allowing Boolean combinations of probabilistic assertions and nested probabilistic formulas. Methods: We introduce a normal form for this problem and show that both nesting of probabilities and multi-agent probabilities do not increase the expressivity of GPSAT. An algorithm to solve GPSAT instances in the normal form via mixed integer linear programming is proposed. Results: The implementation of the algorithm is used to explore the complexity profile of GPSAT, and it shows evidence of phase-transition phenomena. Conclusions: Even though GPSAT is considerably more expressive than PSAT, it can be handled using integer linear programming techniques.

Lecture Notes in Computer Science, 2010

We propose a novel algebraic characterisation of the classical notion of validity for many-valued... more We propose a novel algebraic characterisation of the classical notion of validity for many-valued logics, called entailment multipliers. We demonstrate the existence of such multipliers for many-valued logics in an algebraic presentation of polynomial rings over finite-valued matrices. A set of conditions is present such that, if a logic can express operators satisfying those conditions, than the existence of entailment multipliers is guaranteed. Classical logic is a special case of importance and the existence and computation of entailment multipliers is discussed at length both over boolean rings and over boolean algebras.

IFIP International Federation for Information Processing

In this paper we present an effective prover for mbC, a minimal inconsistency logic. The mbC logi... more In this paper we present an effective prover for mbC, a minimal inconsistency logic. The mbC logic is a paraconsistent logic of the family of logics of formal inconsistency. Paraconsistent logics have several philosophical motivations as well as many applications in Artificial Intelligence such as in belief revision, inconsistent knowledge reasoning, and logic programming. We have implemented the KEMS prover for mbC, a theorem prover based on the KE tableau method for mbC. We show here that the proof system on which this prover is based is sound, complete and analytic. To evaluate the KEMS prover for mbC, we devised four families of mbC-valid formulas and we present here the first benchmark results using these families.

Theoretical Computer Science, 2006

The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning v... more The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249-310] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of propositional letters, approximates classical logic as the size of the set increases. The original proposal dealt only with formulas in clausal form, but in Finger and Wassermann [Approximate and limited reasoning: semantics, proof theory, expressivity and control, J. Logic Comput. 14(2) (2004) 179-204], one of the approximate systems was extended to deal with full propositional logic, giving the new system semantics, an axiomatisation, and a sound and complete proof method based on tableaux. In this paper, we extend another approximate system by Schaerf and Cadoli, presented in a subsequent work [M. Cadoli, M. Schaerf, The complexity of entailment in propositional multivalued logics, Ann. Math. Artif. Intell. 18(1) (1996) 29-50] and then take the idea further, presenting a more general approximation framework of which the previous ones are particular cases, and show how it can be used to formalise heuristics used in theorem proving.

Logic Journal of IGPL, 2008

In this paper we explore a generalization of traditional abduction which can simultaneously perfo... more In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: (i) given an unprovable sequent G, find a sentence H such that ,H G is provable (hypothesis generation); (ii) given a provable sequent G, find a sentence H such that H and the proof of ,H G is simpler than the proof of G (lemma generation). We argue that the two tasks should not be distinguished, and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux.

Logic Journal of IGPL, 2007

This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a... more This work studies the structure of proofs containing non-analytic cuts in the cut-based system, a sequent inference system in which the cut rule is not eliminable and the only branching rule is the cut. Such sequent system is invertible, leading to the KE-tableau decision method. We study the structure of such proofs, proving the existence of a normal form for them in the form of a comb-tree proof. We then concentrate on the problem of efficiently computing non-analytic cuts. For that, we study the generalisation of techniques present in many modern theorem provers, namely the techniques of conflict-driven formula learning.

Logic Journal of IGPL, 2010

Traditional abduction imposes as a precondition the restriction that the background information m... more Traditional abduction imposes as a precondition the restriction that the background information may not derive the goal data. In first-order logic such precondition is, in general, undecidable. To avoid such problem, we present a first-order cutbased abduction method, which has KE-tableaux as its underlying inference system. This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the undecidable precondition problem. After demonstrating the correctness of the method, we show how this method can be dynamically iterated in a process that leads to the construction of non-analytic first-order proofs and, in some terminating cases, to refutations as well.

Logic Journal of IGPL, 1997

Logic Journal of IGPL, 1998

Is it possible to compute in which logics a given formula is deducible? The aim of this paper is ... more Is it possible to compute in which logics a given formula is deducible? The aim of this paper is to provide a formal basis to answer positively this question in the context of substructural logics. Such a basis is founded on structurally-free logic, a logic in which the usual structural rules are replaced by complex combinator rules, and thus constitute a generalization of traditional sequent systems. A family of substructural logics is identified by the set of structural rules admissible to all its members. Combinators encode the sequence of structural rules needed to prove a formula, thus representing the family of logics in which that formula is provable. In this setting, structurallyfree theorem proving is a decision procedure that inputs a formula and outputs the corresponding combinator when the formula is deducible. We then present an algorithm to compute a combinator corresponding to a given formula (if it exists) in the fragment containing only the connectives → and ⊗. The algorithm is based on equistructural transformations , i.e. it transforms one sequent in a set of simpler sequents from which we can compute the combinator (which represents the structure) of the original sequent. We show that this algorithm is sound and complete and always terminates.

Logic Journal of IGPL, 1999

In this paper a uniform methodology to perform natural deduction over the family of linear, relev... more In this paper a uniform methodology to perform natural deduction over the family of linear, relevance and intuitionistic logics is proposed. The methodology follows the Labelled Deductive Systems (LDS) discipline, where the deductive process manipulates declarative units-formulas labelled according to a labelling algebra. In the system described here, labels are either ground terms or variables of a given labelling language and inference rules manipulate formulas and labels simultaneously, generating (whenever necessary) constraints on the labels used in the rules. A set of natural deduction style inference rules is given, and the notion of a derivation is defined which associates a labelled natural deduction style "structural derivation" with a set of generated constraints. Algorithmic procedures, based on a technique called resource abduction, are defined to solve the constraints generated within a structural derivation, and their termination conditions discussed. A natural deduction derivation is then defined to be correct with respect to a given substructural logic, if, under the condition that the algorithmic procedures terminate, the associated set of constraints is satisfied with respect to the underlying labelling algebra. Finally, soundness and completeness of the natural deduction system are proved with respect to the LKE tableaux system [6]. 1

Journal of Logic, Language and Information, 2006

In this paper we study families of resource aware logics that explore resource restriction on rul... more In this paper we study families of resource aware logics that explore resource restriction on rules; in particular, we study the use of controlled cut-rule and introduce three families of parameterised logics that arise from different ways of controlling the use of cut. We start with a formulation of classical logic in which cut is non-eliminable and then impose restrictions on the use of cut. Three Cut-and-Pay families of logics are presented, and it is shown that each family provides an approximation process for full propositional classical logic when the control over the use of cut is progressively weakened. A sound and complete semantics is given for each component of each of the three families of approximated logics. One of these families is shown to possess the uniform substitution property, a new result for approximated reasoning. A tableau based decision procedure is presented for each element of the approximation families and the complexity of each decision procedure is studied. We show that there are families in which every component logic can be decided polynomially.

Journal of Logic and Computation, 2004

Real agents (natural or artificial) are limited in their reasoning capabilities. In this paper, w... more Real agents (natural or artificial) are limited in their reasoning capabilities. In this paper, we present a general framework for modelling limited reasoning based on approximate reasoning and discuss its properties. We start from Cadoli and Schaerf's approximate entailment. We first extend their system to deal with the full language of propositional logic. A tableau inference system is proposed for the extended system together with a subclassical semantics; it is shown that this new approximate reasoning system is sound and complete with respect to this semantics. We show how this system can be incrementally used to move from one approximation to the next until the reasoning limitation is reached. We also present a sound and complete axiomatization of the extended system. We note that although the extension is more expressive than the original system, it offers less control over the approximation process. We then propose a more general system and show that it keeps the increased expressivity and recovers the control. A sound and complete formulation for this new system is given and its expressivity and control advantages are formally proved.

Journal of Logic and Computation, 2006

In this article we present s 1 , a family of logics that is useful to disprove propositional form... more In this article we present s 1 , a family of logics that is useful to disprove propositional formulas by means of an anytime approximation process. The systems follows the paradigm of a parameterized family of logics established by Schaerf's and Cadoli's system S 1. We show that s 1 inherits several of the nice properties of S 1 , while presenting several attractive new properties. The family s 1 deals with the full propositional language, has a complete tableau proof system which provides for incremental approximations; furthermore, it constitutes a full approximation of classical logic from above, with an approximation process with better relevance and locality properties than S 1. When applied to clausal inference, s 1 provides a strong simplification method. An application of s 1 to model-based diagnosis is presented, demonstrating how the solution to this problem can benefit from the use of s 1 approximations.

Journal of Logic and Computation, 2008

The logic of proofs (LP) was proposed as Gödel's missed link between Intuitionistic and S4-proofs... more The logic of proofs (LP) was proposed as Gödel's missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for LP have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for LP that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of LP-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed.

Journal of Applied Logic, 2014

This paper examines two aspects of propositional probabilistic logics: the nesting of probabilist... more This paper examines two aspects of propositional probabilistic logics: the nesting of probabilistic operators, and the expressivity of probabilistic assessments. We show that nesting can be eliminated when the semantics is based on a single probability measure over valuations; we then introduce a classification for probabilistic assessments, and present novel results on their expressivity. Logics in the literature are categorized using our results on nesting and on probabilistic expressivity.

Electronic Notes in Theoretical Computer Science, 2003

The idea of approximate entailment has been proposed in [13] as a way of modeling the reasoning o... more The idea of approximate entailment has been proposed in [13] as a way of modeling the reasoning of an agent with limited resources. They proposed a system in which a family of logics, parameterized by a set of propositional letters, approximates classical logic as the size of the set increases. In this paper, we take the idea further, extending two of their systems to deal with full propositional logic, giving them semantics and sound and complete proof methods based on tableaux. We then present a more general system of which the two previous systems are particular cases and show how it can be used to formalize heuristics used in theorem proving.

Electronic Notes in Theoretical Computer Science, 2009

The KE inference system is a tableau method developed by Marco Mondadori which was presented as a... more The KE inference system is a tableau method developed by Marco Mondadori which was presented as an improvement, in the computational efficiency sense, over Analytic Tableaux. In the literature, there is no description of a theorem prover based on the KE method for the C 1 paraconsistent logic. Paraconsistent logics have several applications, such as in robot control and medicine. These applications could benefit from the existence of such a prover. We present a sound and complete KE system for C 1 , an informal specification of a strategy for the C 1 prover as well as problem families that can be used to evaluate provers for C 1. The C 1 KE system and the strategy described in this paper will be used to implement a KE based prover for C 1 , which will be useful for those who study and apply paraconsistent logics.