# Domenico CantoneUniversity of Catania | UNICT · Department of Mathematics and Computer Science (DMI)

Domenico Cantone

PhD in Computer Science (NYU)

## About

230

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Introduction

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November 1991 - present

## Publications

Publications (230)

This paper enriches a pre-existing decision algorithm, which in turn augmented a fragment of Tarski's elementary algebra with one-argument real functions endowed with a continuous first derivative. In its present (still quantifier-free) version, our decidable language embodies the addition of functions and multiplication of functions by scalars; th...

We describe a model that explains possibly indecisive choice behavior, that is, quasi-choices (choice correspondences that may be empty on some menus). The justification is here provided by a proportion of ballots, which are quasi-choices rationalizable by an arbitrary binary relation. We call a quasi-choice $s$-majoritarian if all options selected...

These slides refer to the authors' ongoing research about a bounded rationality model (majoritarian balloting).
Particularly, the slides are concerned with a presentation at Saarbrucken (Germany) that explains these ideas and poses questions for future research.

The interoperability of devices from distinct brands on the Internet of Things (IoT) domain is still an open issue. The main reason is that pioneer companies always deliberately neglected to deploy devices able to interoperate with competitors products. The key factors that may invert such a trend derive, on one hand, from the abstraction of commun...

In this contribution we extend an ontology for modelling agents and their interactions, called Ontology for Agents, Systems, and Integration of Services (in short, OASIS), with conditionals and ontological smart contracts (in short, OSCs). OSCs are ontological representations of smart contracts that permit to establish responsibilities and authoriz...

Blockchains are gaining momentum due to the interest of industries and people in decentralized applications (Dapps), particularly in those for trading assets through digital certificates secured on blockchain, called tokens. As a consequence, providing a clear unambiguous description of any activities carried out on blockchains has become crucial,...

Decentralized applications (in short, DApps) built on blockchains are disrupting the digital commerce foundations by pursuing new business models based on trustless, decentralized transactions, where intermediaries and central authorities are discarded. One of those emerging means are the digital tokens, certificates emitted and exchanged on the bl...

As a contribution to quantitative set-theoretic inferencing, a translation is proposed of conjunctions of literals of the forms $x=y\setminus z$, $x \neq y\setminus z$, and $z =\{x\}$, where $x,y,z$ stand for variables ranging over the von Neumann universe of sets, into unquantified Boolean formulae of a rather simple conjunctive normal form. The f...

Convex geometries (Edelman and Jamison, 1985) are finite combinatorial structures dual to union-closed antimatroids or learning spaces. We define an operation of resolution for convex geometries, which replaces each element of a base convex geometry by a fiber convex geometry. Contrary to what happens for similar constructions–compounds of hypergra...

The Satisfiability Modulo Theories (SMT) issue concerns the satisfiability of formulae from multiple background theories, usually expressed in the language of first-order predicate logic with equality. SMT solvers are often based on variants of the Nelson-Oppen combination method, a solver for the quantifier-free fragment of the combination of theo...

Blockchains are gaining momentum due to the interest of industries and people in \emph{decentralized applications} (Dapps), particularly in those for trading assets through digital certificates secured on blockchain, called tokens. As a consequence, providing a clear unambiguous description of any activities carried out on blockchains has become cr...

We report on an investigation aimed at identifying small fragments of set theory (typically, sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision tests, potentially useful for automated proof verification. Leaving out of consideration the membership relator ∈ for the time being, in this paper we provide a co...

We describe a process to compose and decompose choice behavior, called resolution. In the forward direction, resolutions amalgamate simple choices to create a complex one. In the backward direction, resolutions detect when and how a primitive choice can be deconstructed into smaller choices. A choice is resolvable if it is the resolution of smaller...

The satisfiability problem for multilevel syllogistic extended with the Cartesian product operator (MLS×) is a long-standing open problem in computable set theory. For long, it was not excluded that such a problem were undecidable, due to its remarkable resemblance with the well-celebrated Hilbert’s tenth problem, as it was deemed reasonable that u...

We present an OWL 2 ontology, called SaintGall, representing the Saint Gall plan, one of the most ancient documents arrived intact to us. The Saint Gall plan describes the ideal model of a Benedictine monastic complex that inspired the design of many European monasteries. The structural, functional, and architectural specification of an ideal Bened...

Convex geometries (Edelman and Jamison, 1985) are finite combinatorial structures dual to union-closed antimatroids or learning spaces. We define an operation of resolution for convex geometries, which replaces each element of a base convex geometry by a fiber convex geometry. Contrary to what happens for similar constructions -- compounds of hyper...

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic 𝒟ℒ〈4LQSR,×〉(D) (𝒟ℒD4,×, for short). Our application solves the main TBox and ABox reasoning problems for 𝒟ℒD4,×. In particular, it solves the consistency and the classification problems for 𝒟ℒD4,×-knowledge...

In this paper we investigate the \emph{approximate string matching problem} when the allowed edit operations are \emph{non-overlapping unbalanced translocations of adjacent factors}. Such kind of edit operations take place when two adjacent sub-strings of the text swap, resulting in a modified string. The two involved substrings are allowed to be o...

In this paper we consider the most common TBox and ABox reasoning services for the description logic 𝒟ℒ〈4LQSR,x〉(D) ( 𝒟 ℒ D 4,× , for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment 4LQSR. 𝒟 ℒ D 4,× is a very expressive description logic. It combines the high scalability and efficienc...

In this contribution we extend an ontology for modelling agents and their interactions, called Ontology for Agents, Systems, and Integration of Services (in short, OASIS), with conditionals and ontological smart contracts (in short, OSCs). OSCs are ontological representations of smart contracts that allow to establish responsibilities and authoriza...

We present a visual, dissection proof for the Pythagorean theorem.

We carry on a long-standing investigation aimed at identifying fragments of set theory that are potentially useful in automated verification with proof-checkers, such as ÆtnaNova, based on the set-theoretic formalism. This note provides a complete taxonomy of the polynomial and the NP-complete fragments consisting of all conjunctions that involve,...

We introduce representations of finite multi-valued choices by possibly indecisive voters. The strict preferences of a voter are modeled by an arbitrary binary relation. We define two forms of social rationality: democracy and liberalism. A choice is democratic if there is a set of voters that rationalizes the selection process by a simple majority...

We present a prototype version of an ontology-based framework, called PROF-ONTO, that integrates IoT devices and users with domotic environments. PROF-ONTO is based on a novel OWL 2 ontology, called OASIS (Ontology for Agents, Systems, and Integration of Services), modelling behaviors of agents such as IoT devices and users, and other information c...

We present a simple and very efficient algorithm for string matching based on the combination of weak factor recognition and hashing. Despite its quadratic worst-case running time, our algorithm exhibits a sublinear behaviour. We also propose some practical improvements of our algorithm and a variant with a linear worst-case time complexity. Experi...

A choice space is a finite set of alternatives endowed with a map associating to each menu a nonempty subset of selected items. A congruence on a choice space is an equivalence relation that preserves its structure. Intuitively, two alternatives are congruent if the agent is indifferent between them, and, in addition, her choice is influenced by th...

Unbalanced translocations are among the most frequent chromosomal alterations, accounted for 30\% of all losses of heterozygosity, a major genetic event causing inactivation of tumor suppressor genes. Despite of their central role in genomic sequence analysis, little attention has been devoted to the problem of matching sequences allowing for this...

Given a pattern x of length m and a text y of length n, both over a totally ordered alphabet, the order-preserving pattern matching (OPPM) problem consists in finding all substrings of the text with the same relative order as the pattern. The OPPM problem, which might be viewed as an approximate variant of the well-known exact pattern matching prob...

We present a KE-tableau-based procedure for the main TBox and ABox reasoning tasks for the description logic \(\mathcal {DL}\langle \mathsf {4LQS^{R,\!\times }}\rangle (\mathbf {D})\), in short \(\mathcal {DL}_{\mathbf {D}}^{4,\!\times }\). The logic \(\mathcal {DL}_{\mathbf {D}}^{4,\!\times }\), representable in the decidable multi-sorted quantifi...

We study a variant of the Ackermann encoding $\mathbb{N}(x) := \sum_{y\in x}2^{\mathbb{N}(y)}$ of the hereditarily finite sets by the natural numbers, applicable to the larger collection $\mathsf{HF}^{1/2}$ of the hereditarily finite hypersets. The proposed variation is obtained by simply placing a `minus' sign before each exponent in the definitio...

We present a \ke-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic $\dlssx$ ($\shdlssx$, for short). Our application solves the main TBox and ABox reasoning problems for $\shdlssx$. In particular, it solves the consistency problem for $\shdlssx$-knowledge bases represented in set...

We present a \ke-based procedure for the main TBox and ABox reasoning tasks for the description logic $\dlssx$, in short $\shdlssx$. The logic $\shdlssx$, representable in the decidable multi-sorted quantified set-theoretic fragment $\flqsr$, combines the high scalability and efficiency of rule languages such as the Semantic Web Rule Language (SWRL...

We present a first result towards the use of entailment in- side relational dual tableau-based decision procedures. To this end, we introduce a fragment of RL(1) which admits a restricted form of composition, (R ; S) or (R ; 1), where the left subterm R of (R ; S) is only allowed to be either the constant 1, or a Boolean term neither containing the...

In connection with the decision problem in set theory, we are interested in specific collections of quantifier-free formulae, referred to as FRAGMENTS or THEORIES throughout the book. These involve various combinations of set-theoretic operators and predicates. In particular, the elementary Boolean set-theoretic operators of binary union ∪, binary...

The analysis of the decision problem for MLSSPF is rather different from that for MLSSP. First of all, an MLSSPF-formula can contain an explicit literal that forces the model to be infinite (e.g., ¬Finite(x)), therefore MLSSPF cannot enjoy the small model property. The second different aspect of this application is that we shall not look for any pa...

Towards a proof of the decidability of MLSSP, there are two fundamental goals to achieve. The first one consists in finding a shadow process that is good enough to create an assignment that L-simulates the original one and, therefore, using Lemma 2.24, also good enough to create a model for the original formula.

We briefly recall some basic set-theoretic terminology which will be used throughout the book.

As seen in the previous chapter, in the case of S-formulae, classical satisfiability by set assignments is equivalent to satisfiability by partitions (cf. Lemma 2.18). In fact, we can further restrict ourselves to satisfiability by 𝒫 -partitions.

This book presents an intuitive picture-oriented approach to the formative processes technique and to its applications. In the first part the authors introduce basic set-theoretic terminology and properties, the decision problem in set theory, and formative processes. The second part of the book is devoted to applications of the technique of format...

In this paper, written to honor the career of Ewa Orłowska, we survey the main results on dual tableau-based decision procedures for fragments of the logic of binary relations. Specifically, we shall review relational fragments representing well known classes of first-order logic, of modal and multi-modal logics, and of description logics. We shall...

We present an OWL 2 ontology representing the Saint Gall plan, one of the most ancient documents arrived intact to us, that describes the ideal model of a Benedictine monastic complex, and that inspired the design of many European monasteries.

Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all elements of A that are deemed selectable by an agent. A choice on U is total if its domain is the powerset of...

Given a set $U$ of alternatives, a choice (correspondence) on $U$ is a contractive map $c$ defined on a family $\Omega$ of nonempty subsets of $U$. Semantically, a choice $c$ associates to each menu $A \in \Omega$ a nonempty subset $c(A) \subseteq A$ comprising all elements of $A$ that are deemed selectable by an agent. A choice on $U$ is total if...

We present an ongoing implementation of a \ke\space based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic $\dlssx$ (shortly $\shdlssx$). The reasoner checks the consistency of $\shdlssx$-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports $\s...

String matching is the problem of finding all the substrings of a text which match a given pattern. It is one of the most investigated problems in computer science, mainly due to its very diverse applications in several fields. Recently, much research in the string matching field has focused on the efficiency and flexibility of the searching proced...

We introduce the Dichotomy Property, a new property of some languages in Set Computable Theory, in order to explore the expressivity of some languages which are extensions of MLS. By-product we prove undecidability of MLS extended with not ordered cartesian product and disjoint unary union operators.

In the last decades, several fragments of set theory have been studied in the context of Computable Set Theory. In general, the semantics of set-theoretic languages differs from the canonical first-order semantics in that the interpretation domain of set-theoretic terms is fixed to a given universe of sets. Because of this, theoretical results and...

In this paper we consider the most common ABox reasoning services for the description logic $\dlssx$ ($\shdlssx$, for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment \flqsr. $\shdlssx$ is a very expressive description logic admitting various concept and role constructs, datatypes, and...

In this contribution, we developed a Linked Open Dataset, more specifically an OWL ontology, about the history of the renovation of the Catania’s Benedictines Monastery by the architect Giancarlo De Carlo. We considered a wide subset of public and private documents collected from 1977 to 2006 during the process of restoration and adaptation of the...

This volume contains the proceedings of the Seventh International Symposium on Games, Automata, Logic and Formal Verification (GandALF 2016). The symposium took place in Catania, Italy, from the 14th to the 16th of September 2016. The proceedings of the symposium contain abstracts of the 3 invited talks and 21 full papers that were accepted after a...

We address the problem of Conjunctive Query Answering (CQA) for the description logic $\dlssx$ ($\shdlssx$, for short) which extends the logic $\dlss$ with Boolean operations on concrete roles and with the product of concepts. The result is obtained by formalizing $\shdlssx$-knowledge bases and $\shdlssx$-conjunctive queries in terms of formulae of...

The way in which Martin Davis conceived the first chapter of his book “Applied nonstandard analysis
” is a brilliant example of information hiding as a guiding principle for the design of widely applicable constructions and methods of proof. We discuss here a common trait that we see between that book and another writing of the year 1977, “Metamath...

Given a pattern and text, both over a common ordered alphabet, the order-preserving pattern matching problem consists in finding all substrings of the text with the same relative order as the pattern. This problem, an approximate variant of the well-known exact pattern matching problem, finds applications in such fields as time series analysis (e.g...

We solve the satisfiability problem for a three-sorted fragment of set theory
(denoted $3LQST_0^R$), which admits a restricted form of quantification over
individual and set variables and the finite enumeration operator $\{\text{-},
\text{-}, \ldots, \text{-}\}$ over individual variables, by showing that it
enjoys a small model property, i.e., any...

In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web.
Specifically, we introduce the description logic \(\mathcal {DL}\langle 4LQS^R\rangle (\mathbf {D})\)–allowing features such as min/max cardinality constructs on the left-hand/right-hand side o...

We present a new adaptive sorting algorithm which is optimal for most
disorder metrics and, more important, has a simple and quick implementation. On
input $X$, our algorithm has a theoretical $\Omega (|X|)$ lower bound and a
$\mathcal{O}(|X|\log|X|)$ upper bound, exhibiting amazing adaptive properties
which makes it run closer to its lower bound a...

The closest string problem (CSP) consists in finding a string t with minimum Hamming distance from the strings of a given finite input set. To overcome its NP-hardness, we propose a simulated annealing approach along with a new heuristic for finding a good initial solution for the problem, which allows one to speed up sensibly the convergence of th...

In the last decades, several fragments of set theory have been studied in the context of the so-called Computable Set Theory. In general, the semantics of set-theoretical languages differs from the canonical first-order semantics in that the interpretation domain of set-theoretical terms is fixed to a given universe of sets, as for instance the von...

We present a first result towards the use of entailment inside relational dual tableau-based decision procedures. To this end, we introduce a fragment of RL(1), called ({1, ≊, ∩}), which admits a restricted form of composition. We prove the decidability of the ({1, ≊, ∩})- fragment by defining a dual tableau-based decision procedure with a suitable...

We present a dual tableau based decision procedure for a class of fragments of the classical relational logic of binary relations. The logics considered share a common language involving a restricted composition operator and infinitely many relational constants which may have the properties of reflexivity, transitivity, and heredity. The constructi...

In this paper we present hybrid algorithms for the single-source shortest-paths (SSSP) and for the all-pairs shortest-paths (APSP) problems, which are asymptotically fast when run on graphs with few destinations of negative-weight arcs. Plainly, the case of graphs with few sources of negative-weight arcs can be handled as well, using reverse graphs...

The approximate string matching problem consists in finding all locations at which a pattern p of length m matches a substring of a text t of length n, after a finite number of given edit operations. In this paper, we investigate such a problem when the edit operations are translocations of adjacent factors of equal length and inversions of factors...

We study translations of dyadic first-order sentences into equalities between relational
expressions. The proposed translation techniques (which work also in the converse
direction) exploit a graphical representation of formulae in a hybrid of the two
formalisms. A major enhancement relative to previous work is that we can cope with the
relational...

In this note we present three efficient variations of the occurrence heuristic, adopted by many exact string matching algorithms and first introduced in the well-known Boyer-Moore algorithm. Our first heuristic, called improved-occurrence heuristic, is a simple improvement of the rule introduced by Sunday in his Quick-Search algorithm. Our second h...

We present an analysis of the remedian, an efficient, known algorithm, for the approximate median selection problem, that is easy to implement. The algorithm can be used for data in an array, as well as for streaming data. In an array it performs in-place, recursively dividing the candidate values into sets of size b, from which exact medians are s...

We introduce a multi-sorted stratified syllogistic, called 4LQSR, admitting variables of four sorts and a restricted form of quantification over variables of the first three sorts, and prove that it has a solvable satisfiability problem by showing that it enjoys a small model property. Then, we consider the fragments (4LQSR)h of 4LQSR, consisting o...

The paper focuses on extending existing decision procedures for set theory and related theories commonly used in mathematics to handle such notions as monotonicity, ordering, inverse functions, etc. After presenting two decision procedures for the basic multilevel syllogistic fragment of set theory and studying the computational complexity of its d...

We show that a collection of three-sorted set-theoretic formulae, denoted
TLQSR and which admits a restricted form of quantification over individual and
set variables, has a solvable satisfiability problem by proving that it enjoys
a small model property, i.e., any satisfiable TLQSR-formula psi has a finite
model whose size depends solely on the si...

Inversions are a class of chromosomal mutations, widely regarded as one of the major mechanisms for reorganizing the genome.In this paper we present a new algorithm for the approximate string matching problem allowing for non-overlapping inversions which runs in O(nm)O(nm) worst-case time and O(m2)O(m2) space, for a character sequence of size nn an...

The successful sequencing of the genoma of various species leads to a great amount of data that need to be managed and analyzed. With the increasing popularity of high-throughput sequencing technolgies, such data require the design of flexible scalable, efficient algorithms and enterprise data structures to be manipulated by both biologists and com...

This paper describes the analysis of a selected testbed of Semantic Web
ontologies, by a SPARQL query, which determines those ontologies that can be
related to the description logic DL , introduced in [4] and
studied in [9]. We will see that a reasonable number of them is expressible
within such computationally efficient language. We expect that, i...

In this paper we address the decision problem for a fragment of set theory
with restricted quantification which extends the language studied in [4] with
pair related quantifiers and constructs, in view of possible applications in
the field of knowledge representation. We will also show that the decision
problem for our language has a non-determinis...

The Pattern Matching problem with Swaps consists in finding all occurrences of a pattern P in a text T, when disjoint local swaps in the pattern are allowed. In the Approximate Pattern Matching problem with Swaps one seeks, for every text location with a swapped match of P, the number of swaps necessary to obtain a match at the location.
In this pa...

We survey two series of results concerning the decidability of fragments of Tarksi's elementary algebra extended with one-argument functions which meet significant properties such as continuity, differentiability, or analyticity. One series of results regards the initial levels of a hierarchy of prenex sentences involving a single function symbol:...

We present a variant of the Davis-Fechter's technique for eliminating quantifiers in first-order logic, aimed at reducing the incidence of irrelevant dependencies in the construction of Skolem terms. The basic idea behind this contribution is to treat as a single syntactic unit every maximal 'quantifier batch', i.e., group of contiguous alike quant...

Inversions are a class of chromosomal mutations, widely regarded as one of the major mechanisms for reorganizing the genome.
In this paper we present a new algorithm for the approximate string matching problem allowing for non-overlapping inversions
which runs in O (nm)\mathcal{O} (nm) worst-case time and O (m2)\mathcal{O} (m^2)-space, for a chara...

We consider fragments of the relational logic RL(1) obtained by posing various constraints on the relational terms involving the operator of composition of relations. These fragments allow to express several non classical logics including modal and description logics. We show how relational dual tableaux can be employed to provide decision procedur...

We present a decision procedure for a quantified fragment of set theory, called ∀0π involving ordered pairs and some operators to manipulate them. When our decision procedure is applied to ∀0π-formulae whose quantifier prefixes have length bounded by a fixed constant, it runs in nondeterministic polynomial-time. Related to the fragment VQ, we also...

This chapter provides an extended survey of inference mechanisms which are candidates for inclusion in the initial endowment of a proof-verifier based on set theory, and points up some efficiency considerations which limit the complexity of the sets
of statements to which each inference mechanism can be applied.
In addition to discourse-manipulati...

This chapter describes in detail the set-based proof-verification system Ref, developed by the authors, and its underlying design. The chapter falls into two parts: (i) An account of the general syntax
and overall structure of proofs acceptable to the verifier. (ii) A listing of the mechanisms actually chosen from the list
of candidate inference me...