ABA Learning is a recent approach for obtaining Assumption-based Argumentation (ABA) frameworks by reasoning with transformation rules from background knowledge and positive/negative examples of concepts of interest. ABA Learning relies on credulous reasoning under a specific semantic notion of extensions for ABA, namely that of stable extensions. In this paper, we newly frame the problem in terms of credulous reasoning under any semantic notion of extensions for ABA. Focusing on admissible, complete, grounded, preferred as well as stable extensions, we present X-ABALearn, a novel parametric algorithm (with X any ABA semantics) based on variants of the transformation rules of ABA Learning and an implementation thereof in Answer Set Programming. Finally, we explore the use of (our implementation of) X-ABALearn on several learning problems, including tabular data and beyond.

This special issue includes a collection of extended and revised versions of papers presented at the 39th Italian Conference on Computational Logic1 (CILC 2024), which was held in Rome at the National Research Council of Italy on June 26–28. The Italian Conference on Computational Logic is the annual meeting of the Italian Association for Logic Programming2 (GULP – Gruppo Ricercatori e Utenti Logic Programming). The Conference, since its first edition, held in Genoa in 1986, has been an important occasion for meeting and exchanging ideas and experiences among national and international researchers and practitioners working in the field of computational logic. CILC 2024 was attended by more than 50 participants from universities and research centres all over Italy, as well as from Austria, Canada, Cyprus, Poland, Romania and the UK. The conference featured 34 presentations, including three invited talks, one tutorial, original contributed papers and papers already published in related venues, covering many aspects of computational logic from fundamental and theoretical results to applications, experimental experiences and system descriptions.

Over the last decade, as we rely more on deep learning technologies to make critical decisions, concerns regarding their safety, reliability and interpretability have emerged. We introduce a novel Neural Argumentative Learning (NAL) architecture that integrates Assumption-Based Argumentation (ABA) with deep learning for image analysis. Our architecture consists of neural and symbolic components. The former segments and encodes images into facts using object-centric learning, while the latter applies ABA learning to develop ABA frameworks enabling predictions with images. Experiments on synthetic data show that the NAL architecture can be competitive with a state-of-the-art alternative.

ABSTRACT The global adoption of artificial intelligence (AI) has increased dramatically in recent years, becoming commonplace in many fields. Such a pervasiveness has led to changes in how AI is perceived, strengthening discussions on its societal consequences. Thus, a new class of requirements for AI‐based solutions emerged. Broadly speaking, those on “explainability” aim to provide a transparent representation of the (often opaque) reasoning method that an AI‐based solution uses when prompted. This work presents a methodology for validating a class of explainable AI (XAI) models, called deterministic rule‐based models, which are used for expressing an explainable approximation of classifiers based on machine learning. The validation methodology combines logical deduction with constraint‐based reasoning in numerical domains, and it either succeeds or returns quantitative estimations of the invalid deviations found. This information allows us to assess the correctness of an XAI model, or in the case of deviations, to evaluate if it still can be deemed acceptable. The validation methodology has been applied to a simulation‐based study where the decision‐making process copes with the spread of SARS‐COV‐2 inside a railway station. The considered case study is a controlled but nontrivial example that shows the overall applicability of the methodology.

Abstract Catamorphisms are functions that are recursively defined on list and trees and, in general, on algebraic data types (ADTs), and are often used to compute suitable abstractions of programs that manipulate ADTs. Examples of catamorphisms include functions that compute size of lists, orderedness of lists, and height of trees. It is well known that program properties specified through catamorphisms can be proved by showing the satisfiability of suitable sets of constrained Horn clauses (CHCs). We address the problem of checking the satisfiability of those sets of CHCs, and we propose a method for transforming sets of CHCs into equisatisfiable sets where catamorphisms are no longer present. As a consequence, clauses with catamorphisms can be handled without extending the satisfiability algorithms used by existing CHC solvers. Through an experimental evaluation on a nontrivial benchmark consisting of many list and tree processing algorithms expressed as sets of CHCs, we show that our technique is indeed effective and significantly enhances the performance of state-of-the-art CHC solvers.

Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much existing work, ABA frameworks are given up-front, in this paper we focus on the problem of automating their learning from background knowledge and positive/negative examples. Unlike prior work, we newly frame the problem in terms of brave reasoning under stable extensions for ABA. We present a novel algorithm based on transformation rules (such as Rote Learning, Folding, Assumption Introduction and Fact Subsumption) and an implementation thereof that makes use of Answer Set Programming. Finally, we compare our technique to state-of-the-art ILP systems that learn defeasible knowledge.

This paper presents some ideas concerning program manipulation and program transformation from the early days of their development. Particular emphasis will be given to program transformation techniques in the area of functional programming and constraint logic programming. We will also indicate current applications of program transformation techniques to the verification of program properties and program synthesis.

The emergence of microservices architecture calls for novel methodologies and technological frameworks that support the design, development, and maintenance of applications structured according to this new architectural style. In this paper, we consider the issue of designing suitable strategies for the governance of testing activities within the microservices paradigm. We focus on the problem of discovering implicit relations between test programs that help to avoid re-running all the available test suites each time one of its constituents evolves. We propose a dynamic analysis technique and its supporting framework that collects information about the invocations of local and remote APIs. Information on test program execution is obtained in two ways: instrumenting the test program code or running a symbolic execution engine. The extracted information is processed by a rule-based automated reasoning engine, which infers implicit similarities among test programs. We show that our analysis technique can be used to support the reduction of test suites, and therefore has good application potential in the context of regression test optimisation. The proposed approach has been validated against two real-world microservices applications.

Abstract We address the problem of checking the satisfiability of constrained Horn clauses (CHCs) defined on algebraic data types (ADTs), such as lists and trees. We propose a new technique for transforming CHCs defined on ADTs into CHCs where the arguments of the predicates have only basic types, such as integers and booleans. Thus, our technique avoids, during satisfiability checking, the explicit use of proof rules based on induction over the ADTs. The main extension over previous techniques for ADT removal is a new transformation rule, called differential replacement, which allows us to introduce auxiliary predicates, whose definitions correspond to lemmas that are used when making inductive proofs. We present an algorithm that performs the automatic removal of ADTs by applying the new rule, together with the traditional folding/unfolding rules. We prove that, under suitable hypotheses, the set of the transformed clauses is satisfiable if and only if so is the set of the original clauses. By an experimental evaluation, we show that the use of the new rule significantly improves the effectiveness of ADT removal. We also show that our approach is competitive with respect to tools that extend CHC solvers with the use of inductive rules.

Abstract This paper surveys recent work on applying analysis and transformation techniques that originate in the field of constraint logic programming (CLP) to the problem of verifying software systems. We present specialization-based techniques for translating verification problems for different programming languages, and in general software systems, into satisfiability problems for constrained Horn clauses (CHCs), a term that has become popular in the verification field to refer to CLP programs. Then, we describe static analysis techniques for CHCs that may be used for inferring relevant program properties, such as loop invariants. We also give an overview of some transformation techniques based on specialization and fold/unfold rules, which are useful for improving the effectiveness of CHC satisfiability tools. Finally, we discuss future developments in applying these techniques.

Abstract We address the problem of verifying that the functions of a program meet their contracts, specified by pre/postconditions. We follow an approach based on constrained Horn clauses (CHCs) by which the verification problem is reduced to the problem of checking satisfiability of a set of clauses derived from the given program and contracts. We consider programs that manipulate algebraic data types (ADTs) and a class of contracts specified by catamorphisms, that is, functions defined by simple recursion schemata on the given ADTs. We show by several examples that state-of-the-art CHC satisfiability tools are not effective at solving the satisfiability problems obtained by direct translation of the contracts into CHCs. To overcome this difficulty, we propose a transformation technique that removes the ADT terms from CHCs and derives new sets of clauses that work on basic sorts only, such as integers and booleans. Thus, when using the derived CHCs there is no need for induction rules on ADTs. We prove that the transformation is sound, that is, if the derived set of CHCs is satisfiable, then so is the original set. We also prove that the transformation always terminates for the class of contracts specified by catamorphisms. Finally, we present the experimental results obtained by an implementation of our technique when verifying many non-trivial contracts for ADT manipulating programs.

We present an operational semantics for time-aware business processes, that is, processes modeling the execution of business activities, whose durations are subject to linear constraints over the integers. We assume that some of the durations are controllable, that is, they can be determined by the organization that executes the process, while others are uncontrollable, that is, they are determined by the external world. Then, we consider controllability properties, which guarantee the completion of the execution of the process, satisfying the given duration constraints, independently of the values of the uncontrollable durations. Controllability properties are encoded by quantified reachability formulas, where the reachability predicate is recursively defined by means of constrained Horn clauses (CHCs). These clauses are automatically derived from the operational semantics of the process. Finally, we present two algorithms for solving the so called weak and strong controllability problems. Our algorithms reduce these problems to the verification of a set of quantified integer constraints, which are simpler than the original quantified reachability formulas, and can effectively be handled by state-of-the-art CHC solvers.

Abstract It is well-known that the verification of partial correctness properties of imperative programs can be reduced to the satisfiability problem for constrained Horn clauses (CHCs). However, state-of-the-art solvers for constrained Horn clauses (or CHC solvers) based onpredicate abstractionare sometimes unable to verify satisfiability because they look for models that are definable in a given class 𝓐 of constraints, called 𝓐-definable models. We introduce a transformation technique, calledPredicate Pairing, which is able, in many interesting cases, to transform a set of clauses into an equisatisfiable set whose satisfiability can be proved by finding an 𝓐-definable model, and hence can be effectively verified by a state-of-the-art CHC solver. In particular, we prove that, under very general conditions on 𝓐, the unfold/fold transformation rules preserve the existence of an 𝓐-definable model, that is, if the original clauses have an 𝓐-definable model, then the transformed clauses have an 𝓐-definable model. The converse does not hold in general, and we provide suitable conditions under which the transformed clauses have an 𝓐-definable modelif and only ifthe original ones have an 𝓐-definable model. Then, we present a strategy, called Predicate Pairing, which guides the application of the transformation rules with the objective of deriving a set of clauses whose satisfiability problem can be solved by looking for 𝓐-definable models. The Predicate Pairing (PP) strategy introduces a new predicate defined by the conjunction of two predicates occurring in the original set of clauses, together with a conjunction of constraints. We will show through some examples that an 𝓐-definable model may exist for the new predicate even if it does not exist for its defining atomic conjuncts. We will also present some case studies showing that Predicate Pairing plays a crucial role in the verification ofrelational properties of programs, that is, properties relating two programs (such as program equivalence) or two executions of the same program (such as non-interference). Finally, we perform an experimental evaluation of the proposed techniques to assess the effectiveness of Predicate Pairing in increasing the power of CHC solving.

Abstract We address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees. We propose a transformation technique whose objective is the removal of these data structures from CHCs, hence reducing their satisfiability to a satisfiability problem for CHCs on integers and booleans. We propose a transformation algorithm and identify a class of clauses where it always succeeds. We also consider an extension of that algorithm, which combines clause transformation with reasoning on integer constraints. Via an experimental evaluation we show that our technique greatly improves the effectiveness of applying the Z3 solver to CHCs. We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.

The transformation of constraint logic programs (CLP programs) has been shown to be an effective methodology for verifying properties of imperative programs. By following this methodology, we encode the negation of a partial correctness property of an imperative program prog as a predicate incorrec t defined by a CLP program T, and we show that prog is correct by transforming T into the empty program (and thus incorrect does not hold) through the application of semantics preserving transformation rules. We can also show that prog is incorrect by transforming T into a program with the fact incorrect (and thus incorrect does hold). Some of the transformation rules perform replacements of constraints that are based on properties of the data structures manipulated by the program prog. In this paper we show that Constraint Handling Rules (CHR) are a suitable formalism for representing and applying constraint replacements during the transformation of CLP programs. In particular, we consider programs that manipulate integer arrays and we present a CHR encoding of a constraint replacement strategy based on the theory of arrays. We also propose a novel generalization strategy for constraints on integer arrays that combines CHR constraint replacements with various generalization operators on integer constraints, such as widening and convex hull. Generalization is controlled by additional constraints that relate the variable identifiers in the imperative program prog and the CLP representation of their values. The method presented in this paper has been implemented and we have demonstrated its effectiveness on a set of benchmark programs taken from the literature.

We present a method for automatically generating verification conditions for a class of imperative programs and safety properties. Our method is parametric with respect to the semantics of the imperative programming language, as it specializes, by using unfold/fold transformation rules, a Horn clause interpreter that encodes that semantics.

We present a method for verifying properties of imperative programs that manipulate integer arrays. Imperative programs and their properties are represented by using Constraint Logic Programs (CLP) over integer arrays. Our method is refutational. Given a Hoare triple {ϕ} prog {ψ} that defines a par tial correctness property of an imperative program prog, we encode the negation of the property as a predicate incorrect defined by a CLP program P, and we show that the property holds by proving that incorrect is not a consequence of P. Program verification is performed by applying a sequence of semantics preserving transformation rules and deriving a new CLP program T such that incorrect is a consequence of P iff it is a consequence of T. The rules are applied according to an automatic strategy whose objective is to derive a program T that satisfies one of the following properties: either (i) T is the empty set of clauses, hence proving that incorrect does not hold and prog is correct, or (ii) T contains the fact incorrect, hence proving that prog is incorrect. Our transformation strategy makes use of an axiomatization of the theory of arrays for the manipulation of array constraints, and also applies the widening and convex hull operators for the generalization of linear integer constraints. The strategy has been implemented in the VeriMAP transformation system and it has been shown to be quite effective and efficient on a set of benchmark array programs taken from the literature.

Abstract We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a programprog, we consider a partial correctness specification of the form {ϕ},prog{ψ}, where the assertions ϕ and ψ are predicates defined by a setSpecof possibly recursive Horn clauses with linear arithmetic (LA) constraints in their premise (also calledconstrained Horn clauses). The verification method consists in constructing a setPCof constrained Horn clauses whose satisfiability implies that {ϕ},prog, {ψ} is valid. We highlight some limitations of state-of-the-art constrained Horn clause solving methods, here calledLA-solving methods, which prove the satisfiability of the clauses by looking for linear arithmetic interpretations of the predicates. In particular, we prove that there exist some specifications that cannot be proved valid by any of thoseLA-solving methods. These specifications require the proof of satisfiability of a setPCof constrained Horn clauses that containnonlinear clauses(that is, clauses with more than one atom in their premise). Then, we present a transformation, calledlinearization, that convertsPCinto a set oflinearclauses (that is, clauses with at most one atom in their premise). We show that several specifications that could not be proved valid byLA-solving methods, can be proved valid after linearization. We also present a strategy for performing linearization in an automatic way and we report on some experimental results obtained by using a preliminary implementation of our method.

We present a method for verifying properties of imperative programs by using techniques based on the specialization of constraint logic programs (CLP). We consider a class of C programs with integer variables and we focus our attention on safety properties, stating that no error configuration can be reached from the initial configurations. We encode the interpreter of the language as a CLP program I, and we also encode the safety property to be verified as the negation of a predicate unsafe defined in I. Then, we specialize the CLP program I with respect to the given C program and the given initial and error configurations, with the objective of deriving a new CLP program I_sp which either contains the fact 'unsafe' (and in this case the C program is proved unsafe) or contains no clauses with head 'unsafe' (and in this case the C program is proved safe). If I_sp does not enjoy this property we iterate the specialization process with the objective of deriving a CLP program where we can prove unsafety or safety. During the various specializations we may apply different strategies for propagating information (either propagating forward from an initial configuration, or propagating backward from an error configuration) and different operators (such as widening and convex hull operators) for generalizing predicate definitions. Due to the undecidability of program safety, the iterated specialization process may not terminate. By an experimental evaluation carried out on a set of examples taken from the literature, we show that our method is competitive with respect to state-of-the-art software model checkers.

We address the problem of the automatic synthesis of concurrent programs within a framework based on Answer Set Programming (ASP). Every concurrent program to be synthesized is specified by providing both the behavioural and the structural properties