Agata Ciabattoni - Academia.edu (original) (raw)

Papers by Agata Ciabattoni

ACM Transactions on Computational Logic, Apr 2, 2018

Building on ideas of Haskell Curry, in 1969 William Howard showed that constructing an intuitioni... more Building on ideas of Haskell Curry, in 1969 William Howard showed that constructing an intuitionistic proof is not at all different from writing a program in λ-calculus [8]. He also showed that the reduction of the proof to its normal form exactly corresponds to the evaluation of the associated program. This relation between intuitionistic natural deduction and simply typed λ-calculus is now called the Curry–Howard correspondence. In 1990 Griffin showed that such a correspondence is not limited to intuitionistic logic but a similar relation holds between classical logic and sequential extensions of simply typed λ-calculus featuring control operators [7]. One year later, in 1991, Avron noticed a connection between concurrent computation and hypersequent calculus – a proof calculus well suited for capturing logics intermediate between intuituionistic and classical logic, see [3]. He envisaged, in particular, the possibility of using the intermediate logics that can be captured by hype...

We introduce a new proof-theoretic framework which enhances the expressive power of bunched seque... more We introduce a new proof-theoretic framework which enhances the expressive power of bunched sequents by extending them with a hypersequent structure. A general cut-elimination theorem that applies to bunched hypersequent calculi satisfying general rule conditions is then proved. We adapt the methods of transforming axioms into rules to provide cutfree bunched hypersequent calculi for a large class of logics extending the distributive commutative Full Lambek calculus DFLe and Bunched Implication logic BI. The methodology is then used to formulate new logics equipped with a cutfree calculus in the vicinity of Boolean BI.

ACM SIGLOG News, 2018

The interdisciplinary workshop 'Deontic Reasoning: from Ancient Texts to Artificial Intellige... more The interdisciplinary workshop 'Deontic Reasoning: from Ancient Texts to Artificial Intelligence' (ATAI), bringing together experts from the fields of Logic, Sanskrit, Philosophy, Artificial Intelligence and Law, was held at the Vienna University of Technology (TU Wien) on June 11-13, 2018. In nuce , the aim of the workshop was to foster new connections between the aforementioned research areas and facilitate the interchange of ideas with respect to shared grounds of interest, in particular normative reasoning.

Electronic Proceedings in Theoretical Computer Science, 2018

We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a ... more We introduce a first proofs-as-parallel-programs correspondence for classical logic. We define a parallel and more powerful extension of the simply typed λ-calculus corresponding to an analytic natural deduction based on the excluded middle law. The resulting functional language features a natural higher-order communication mechanism between processes, which also supports broadcasting. The normalization procedure makes use of reductions that implement novel techniques for handling and transmitting process closures.

Electronic Notes in Theoretical Computer Science, 2017

The addition of the bounded contraction rules to Full Lambek Calculus with exchange and weakening... more The addition of the bounded contraction rules to Full Lambek Calculus with exchange and weakening (FL ew) gives rise to serious complications for proof search. For example, adding to FL ew a naive version of these rules brakes cut-admissibility. Although this can be avoided by refining these rules, in this work we show that even "good" proof systems for FL ew plus bounded contraction do not necessarily lead to good implementations. In order to solve this problem, we propose an extension of the lazy splitting methodology to bounded contractions, showing how to transform our focused, cut-free sequent calculus into a terminating theorem prover. Our system is used to show that the decision problem for FL ew with bounded contraction is in EXPTIME.

Lecture Notes in Computer Science, 2006

The cornerstone for the success of Service-Oriented Computing lies in its promise to allow fast a... more The cornerstone for the success of Service-Oriented Computing lies in its promise to allow fast and easy composition of services to create added-value applications. Compositions need to be described in terms of their desired functional properties, but the non-functional properties are of paramount importance as well. Inspired by the Web Service challenge we propose a new model for describing the Quality of Service (QoS) of a composition which considers the information flow and describes basic service qualities at the granularity level of service part names, that is, operations comprised in service invocation/response messages. In this initial investigation, we overview a number of formal methods techniques that allow to reason with QoS composition based on the proposed model, and propose an algorithm for determining the QoS of a composition given the QoS associated with the individual services.

International Journal of Approximate Reasoning, 2013

There is no established formal framework for expert systems based on weighted IF-THEN rules. We d... more There is no established formal framework for expert systems based on weighted IF-THEN rules. We discuss three mathematical models that have been recently proposed by the authors for CADIAG-2-a well-known system of this kind. The three frameworks are based on fuzzy logics, probability theory and possibilistic logic, respectively. CADIAG-2 is used here as a case study to evaluate these frameworks. We point out their use, advantages and disadvantages. In addition, the described models provide insight into various aspects of CADIAG-2.

For decades, the gentle murder paradox has been a central challenge for deontic logic. This artic... more For decades, the gentle murder paradox has been a central challenge for deontic logic. This article investigates its millennia-old counterpart in Sanskrit philosophy: the śyena controversy. We analyze three solutions provided by Mı̄mām. sā, the Sanskrit philosophical school devoted to the analysis of normative reasoning in the Vedas, in which the controversy originated. We introduce axiomatizations and semantics for the modal logics formalizing the deontic theories of the main Mı̄mām. sā philosophers Prabhākara, Kumārila, and Man.d. ana. The resulting logics are used to analyze their distinct solutions to the śyena controversy, which we compare with formal approaches developed within the contemporary field of deontic logic.

The satisfiability problem for monadic infinite-valued Gödel logic is known to be undecidable. We... more The satisfiability problem for monadic infinite-valued Gödel logic is known to be undecidable. We identify a fragment of this logic extended with strong negation whose satisfiability is not only decidable but it is decidable within classical logic. We use this fragment to formalize the rules of CADIAG-2, a well performing fuzzy expert system assisting in the differential diagnosis in internal medicine. A (classical) satisfiability check of the resulting formulas allowed the detection of some errors in the rules of the system.

We present a general framework that allows to construct systematically analytic calculi for a lar... more We present a general framework that allows to construct systematically analytic calculi for a large family of (propositional) many-valued logics — called projective logics — characterized by a special format of their semantics. All finite-valued logics as well as infinite-valued Godel logic are projective. As a case-study, sequent of relations calculi for Godel logics are derived. A comparison with some

Abstract. It is shown that G, <SUB>", the quanti ed propositional G?odel logic based o... more Abstract. It is shown that G, <SUB>", the quanti ed propositional G?odel logic based on the truth-value set V<SUB>" = f1 1=n : n 1g [f1g, is decidable. This result is obtained by reduction to B?uchi's theory S1S. An alternative proof based on elimination of quanti ers is also given, which yields both an axiomatization and a characterization of G,

Logic Programming and Automated Reasoning/Russian Conference on Logic Programming, 2004

We provide uniform and invertible logical rules in a framework of re- lational hypersequents for ... more We provide uniform and invertible logical rules in a framework of re- lational hypersequents for the three fundamental t-norm based fuzzy logics i.e., Ëukasiewicz logic, Godel logic, and Product logic. Relati onal hypersequents gen- eralize both hypersequents and sequents-of-relations. Such a framework can be interpreted via a particular class of dialogue games combined with bets, where the rules reflect possible

Fuzzy Sets and Systems, 2015

We provide a methodology to introduce proof search oriented calculi for a large class of many-val... more We provide a methodology to introduce proof search oriented calculi for a large class of many-valued logics, and a sufficient condition for their Co-NP completeness. Our results apply to many well known logics including Gödel, Lukasiewicz and Product Logic, as well as Hájek's Basic Fuzzy Logic.

Lecture Notes in Computer Science, 1999

... of the schematic formulas of the rule. We write α[F/p] for the formula that arises by instant... more ... of the schematic formulas of the rule. We write α[F/p] for the formula that arises by instantiating the formula vari-able p of the schema α[p]. Page 3. 260 Matthias Baaz et al. 3 Two General Undecidability Results ... Page 5. 262 Matthias Baaz et al. we conclude that ...

Lecture Notes in Computer Science, 2002

We present a Schütte-Tait style cut-elimination proof for the hypersequent calculus HIF for first... more We present a Schütte-Tait style cut-elimination proof for the hypersequent calculus HIF for first-order Gödel logic. This proof allows to bound the depth of the resulting cut-free derivation by 4 |d| ρ(d) , where |d| is the depth of the original derivation and ρ(d) the maximal complexity of cut-formulas in it. We compare this Schütte-Tait style cut-elimination proof to a Gentzen style proof.

Lecture Notes in Computer Science, 1998

... of residuation; the weaker of these logics coincides with C. To obtain a cut-free calculus ..... more ... of residuation; the weaker of these logics coincides with C. To obtain a cut-free calculus ... In particular, linearity of truth values - a crucial property of all fuzzy logics - can be enforced on ... logics without linearity; in our case, they will be contraction-free fragments of intuitionistic logic. ...

Lecture Notes in Computer Science, 2001

Herbrand's Theorem for £ ¥ ¤ ¦ , i.e., Gödel logic enriched by the projection operator § is prove... more Herbrand's Theorem for £ ¥ ¤ ¦ , i.e., Gödel logic enriched by the projection operator § is proved. As a consequence we obtain a "chain normal form" and a translation of prenex £ ¤ ¦ into (order) clause logic, referring to the classical theory of dense total orders with endpoints. A chaining calculus provides a basis for efficient theorem proving.

Lecture Notes in Computer Science, 2008

Efficient, automated elimination of cuts is a prerequisite for proof analysis. The method CERES, ... more Efficient, automated elimination of cuts is a prerequisite for proof analysis. The method CERES, based on Skolemization and resolution has been successfully developed for classical logic for this purpose. We generalize this method to Gödel logic, an important intermediate logic, which is also one of the main formalizations of fuzzy logic. RESolution. logic . We show that essential features of CERES can be adapted to the calculus HG [1, for G that uses hypersequents, a generalization of Gentzen's sequents to multisets of sequents. This adaption is far from trivial and, among other novel features, entails a new concept of 'resolution': hyperclause resolution, which combines most general unification and cuts on atomic hypersequents. It also provides clues to a better understanding of resolution based cut elimination for sequent and hypersequent calculi, in general.

Lecture Notes in Computer Science, 2007

The monadic fragments of first-order Gödel logics are investigated. It is shown that all finite-v... more The monadic fragments of first-order Gödel logics are investigated. It is shown that all finite-valued monadic Gödel logics are decidable; whereas, with the possible exception of one (G ↑ ), all infinitevalued monadic Gödel logics are undecidable. For the missing case G ↑ the decidability of an important sub-case, that is well motivated also from an application oriented point of view, is proven. A tight bound for the cardinality of finite models that have to be checked to guarantee validity is extracted from the proof. Moreover, monadic G ↑ , like all other infinite-valued logics, is shown to be undecidable if the projection operator is added, while all finite-valued monadic Gödel logics remain decidable with .