Papers by Camillo Fiorentini
From Constructivism to Logic Programming: an Homage to Mario Ornaghi
Fundamenta Informaticae
Goal-Oriented Proof-Search in Natural Deduction for Intuitionistic Propositional Logic
Journal of Automated Reasoning
Fundamenta Informaticae, 2017
JTabWb is a Java framework for developing provers based on terminating sequent or tableau calculi... more JTabWb is a Java framework for developing provers based on terminating sequent or tableau calculi. It provides a generic engine which performs proof-search driven by a user-defined specification. The user is required to define the components of a prover by implementing suitable Java interfaces. The implemented provers can be used as standalone applications or embedded in other Java applications. The framework also supports proof-trace generation, L A T E X rendering of proofs and counter-model generation.
[FORMULA]: Basic Constructive Description Logic
Journal of Automated Reasoning, 2010
Towards Proof Theoretic Model Generation
Abstract. In recent years model generation tools have been developed in differ-ent areas, such as... more Abstract. In recent years model generation tools have been developed in differ-ent areas, such as DLV or Smodels in the context of Answer Set Programming, or USE in the context of the UML modeling language. In the latter case those models are known as snapshots and ...
Towards introducing types in DLV* (extended abstract)
The advantages of static type checking in programming languages are almost univer- sally recogniz... more The advantages of static type checking in programming languages are almost univer- sally recognized and well-understood, although they made it into logic programming somewhat belatedly (13). From the pioneering paper (11) advocating the introduction of types in Prolog, different approaches emerged, belonging roughly to two main camps: the descriptive and the prescriptive one. The former aims to capture some aspects
All Intermediate Logics with Extra Axions in One Variable, Except Eight, Are Not Strongly omega-Complete
Journal of Symbolic Logic, 2000
In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, e... more In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly $\omega$-complete. Thus, a definitive classification of such logics with respect to
Fundamenta Informaticae, 2015
Focusing is a proof-theoretic device to structure proof search in the sequent calculus: it provid... more Focusing is a proof-theoretic device to structure proof search in the sequent calculus: it provides a normal form to cut-free proofs in which the application of invertible and non-invertible inference rules is structured in two separate and disjoint phases. Although stemming from proofsearch considerations, focusing has not been thoroughly investigated in actual theorem proving, in particular w.r.t. termination. We present a contraction-free (and hence terminating) focused multisuccedent sequent calculus for propositional intuitionistic logic, which refines the G4ip calculus in the tradition of Vorob'ev, Hudelmeier and Dyckhoff. We prove completeness of the calculus semantically and argue that this offers a viable alternative to other more syntactical means.
Proof-Search in Natural Deduction Calculus for Classical Propositional Logic
Lecture Notes in Computer Science, 2015
We give an algorithm solving combined word problems (over non necessarily disjoint signatures) ba... more We give an algorithm solving combined word problems (over non necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth-Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both constructible over their common reduct (on which we do not make any special assumption) .
Lecture Notes in Computer Science, 2002
We present tableau calculi for the logics D k (k ≥ 2) semantically characterized by the classes o... more We present tableau calculi for the logics D k (k ≥ 2) semantically characterized by the classes of Kripke models built on finite k-ary trees. Our tableau calculi use the signs T and F, some tableau rules for Intuitionistic Logic and two rules formulated in a hypertableau fashion. We prove the Soundness and Completeness Theorems for our calculi. Finally, we use them to prove the main properties of the logics D k , in particular their constructivity and their decidability.
Lecture Notes in Computer Science, 2013
We present Gbu, a terminating variant of the sequent calculus G3i for intuitionistic propositiona... more We present Gbu, a terminating variant of the sequent calculus G3i for intuitionistic propositional logic. Gbu modifies G3i by annotating the sequents so to distinguish rule applications into two phases: an unblocked phase where any rule can be backward applied, and a blocked phase where only right rules can be used. Derivations of Gbu have a trivial translation into G3i. Rules for right implication exploit an evaluation relation, defined on sequents; this is the key tool to avoid the generation of branches of infinite length in proof-search. To prove the completeness of Gbu, we introduce a refutation calculus Rbu for unprovability dual to Gbu. We provide a proof-search procedure that, given a sequent as input, returns either a Rbu-derivation or a Gbu-derivation of it.
Lecture Notes in Computer Science, 2010
We present fCube, a theorem prover for Intuitionistic propositional logic based on a tableau calc... more We present fCube, a theorem prover for Intuitionistic propositional logic based on a tableau calculus. The main novelty of fCube is that it implements several optimization techniques that allow to prune the search space acting on different aspects of proof-search. We tested the efficiency of our techniques by comparing fCube with other theorem provers. We found that our prover outperforms the other provers on several interesting families of formulas.
An Evaluation-Driven Decision Procedure for G3i
ACM Transactions on Computational Logic, 2015
ABSTRACT
Lecture Notes in Computer Science, 2004
A tableau calculus for a logic with constructive negation and an implementation of the related de... more A tableau calculus for a logic with constructive negation and an implementation of the related decision procedure is presented. This logic is an extension of Nelson logic and it has been used in the framework of program verification and timing analysis of combinatorial circuits. The decision procedure is tailored to shrink the search space of proofs and it is proved correct by using a semantical technique. It has been implemented in C++ language.
A Constructive Approach to Testing Model Transformations
Lecture Notes in Computer Science, 2010
Abstract. This paper concerns a formal encoding of the Object Management Group&#x... more Abstract. This paper concerns a formal encoding of the Object Management Group's Complete Meta-Object Facility (CMOF) in order to provide a more trust-worthy software development lifecycle for Model Driven Architecture (MDA). We show how a form of constructive logic can be ...
Testing model transformations through metaobject snapshot generation
Dipartimento di Scienze dell’Informazione
We give an algorithm solving combined word problems (over non necessarily disjoint signatures) ba... more We give an algorithm solving combined word problems (over non necessarily disjoint signatures) based on rewriting of equivalence classes of terms. The canonical rewriting system we introduce consists of few transparent rules and is obtained by applying Knuth-Bendix completion procedure to presentations of pushouts among categories with products. It applies to pairs of theories which are both constructible over their common reduct (on which we do not make any special assumption). * Lavoro svolto nell'ambito del progetto MURST "Logica".
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Papers by Camillo Fiorentini