Set Of Clauses Research Articles

Impact of European Integration on Substantive and Formal Constitutional Amendments in Spain in the Light of the Spanish Constitutional Court’s Jurisprudence and Constitutional Practice

The purpose of the article is to answer the question of how the process of European integration has influenced the Spanish constitutional order. Taking the European clause set out in Article 93 of the Spanish Constitution as a starting point, it analyzes both impacts of a formal-legal nature, but also influences of a substantive nature affecting the normative content of the Spanish Constitution. The study demonstrates that EU law, based on the principle of “direct applicability” and “direct effect,” intensively influences Spanish constitutional law and has been the strongest factor influencing the Spanish legal order since the enactment of the Spanish Constitution in 1978. Thus, while the Spanish Constitution in the formal sense remains a rigid constitution, when viewed in the category of a substantive constitution, it has proved to be flexible and susceptible to external influence, despite the fact that this occurs de jure with the consent of Spain expressed in respect of the principle of state sovereignty, on the basis of the provisions contained in Article 93 of the Spanish Constitution.

Cnosso, a novel method for business document automation based on open information extraction

The state-of-the-art in automated processing of unstructured business documents has evolved from manual labor to advanced AI systems in the span of mere decades. Such systems involve learning techniques, rule or clause sets, neural models – either used alone or in combination – for the extraction to work. As an example, rule-based processes operate on a perceived layout or positioning of the information, whereas model-based frameworks adopt a semantic, and often uninspectable, approach. Verb-Based Semantic Role Labeling (VBSRL) is a novel system presented in a former paper that uses a hybrid foundation to inform the extraction phase via a set of rules modeling natural language. We propose a new VBSRL-based document processing method, aided by valuable and innovative architectural choices, which has been implemented for the Italian language and experimented upon with promising results. Even in its infancy, in fact, the first implementation of this system shows better results than comparable IE solutions, obtaining an aggregate, average F-measure of nearly 79%.

Complexity of manipulation and bribery in premise-based judgment aggregation with simple formulas

Judgment aggregation is a framework to aggregate individual opinions on multiple, logically connected issues into a collective outcome. It is open to manipulative attacks such as Manipulation where judges (e.g., referees, experts, or jurors) cast their judgments strategically. Previous works have shown that most computational problems corresponding to these manipulative attacks are NP-hard. This desired computational barrier, however, often relies on formulas that are either of unbounded size or of complex structure.We revisit the computational complexity for various Manipulation and Bribery problems in premise-based judgment aggregation, now focusing on simple and realistic formulas. We restrict all formulas to be clauses that are monotone, Horn-clauses, or have bounded length. We show that these restrictions make several variants of Manipulation and Bribery, which were in general known to be NP-hard, polynomial-time solvable. Moreover, we provide a P vs. NP dichotomy for a large class of clause restrictions (generalizing monotone and Horn clauses).

Dagster: Parallel Structured Search

We demonstrate Dagster, a system that implements a new approach to scheduling interdependent (Boolean) SAT search activities in high-performance computing (HPC) environments. Our system takes as input a set of disjunctive clauses (i.e., DIMACS CNF) and a labelled directed acyclic graph (DAG) structure describing how the clauses are decomposed into a set of interrelated problems. Component problems are solved using standard systematic backtracking search, which may optionally be coupled to (stochastic dynamic) local search and/or clause-strengthening processes. We demonstrate Dagster using a new Graph Maximal Determinant combinatorial case study. This demonstration paper presents a new case study, and is adjunct to the longer accepted manuscript at the Pacific Rim International Conference on Artificial Intelligence (2022).

A Deletion Algorithm for the Marginal Problem in Propositional Logic Based on Boolean Arrays

This paper proposes a deletion algorithm for the marginal problem in propositional logic. The algorithm is based on the general Davis and Putnam deletion algorithm DP, expressed as a bucket elimination algorithm, representing sets of clauses with the same set of variables employing a Boolean array. The main contribution is the development of alternative procedures when deleting a variable which allow more efficient computations. In particular, it takes advantage of the case in which the variable to delete is determined by a subset of the rest of the variables. It also provides a set of useful results and tools for reasoning with Boolean tables. The algorithms are implemented using Python and the NumPy library. Experiments show that this procedure is feasible for intermediate problems and for difficult problems from hard Bayesian networks cases

SAT-Inspired Eliminations for Superposition

Optimized SAT solvers not only preprocess the clause set, they also transform it during solving as inprocessing. Some preprocessing techniques have been generalized to first-order logic with equality. In this article, we port inprocessing techniques to work with superposition, a leading first-order proof calculus, and we strengthen known preprocessing techniques. Specifically, we look into elimination of hidden literals, variables (predicates), and blocked clauses. Our evaluation using the Zipperposition prover confirms that the new techniques usefully supplement the existing superposition machinery.

CHC-COMP 2022: Competition Report

CHC-COMP 2022 is the fifth edition of the competition of solvers for Constrained Horn Clauses. The competition was run in March 2022; the results were presented at the 9th Workshop on Horn Clauses for Verification and Synthesis held in Munich, Germany, on April 3, 2022. This edition featured six solvers, and eight tracks consisting of sets of linear and nonlinear clauses with constraints over linear integer arithmetic, linear real arithmetic, arrays, and algebraic data types. This report provides an overview of the organization behind the competition runs: it includes the technical details of the competition setup as well as presenting the results of the 2022 edition.

Contract Strengthening through Constrained Horn Clause Verification

The functional properties of a program are often specified by providing a contract for each of its functions. A contract of a function consists of a pair of formulas, called a precondition and a postcondition, which, respectively, should hold before and after execution of that function. It might be the case that the contracts supplied by the programmer are not adequate to allow a verification system to prove program correctness, that is, to show that for every function, if the precondition holds and the execution of the function terminates, then the postcondition holds. We address this problem by providing a technique which may strengthen the postconditions of the functions, thereby improving the ability of the verifier to show program correctness. Our technique consists of four steps. First, the translation of the given program, which may manipulate algebraic data structures (ADTs), and its contracts into a set of constrained Horn clauses (CHCs) whose satisfiability implies the validity of the given contracts. Then, the derivation, via CHC transformation performed by the VeriCaT tool, of a new set of CHCs that manipulate only basic sorts (such as booleans or integers) and whose satisfiability implies the satisfiability of the original set of clauses. Then, the construction of a model, if any, of the new, derived CHCs using the CHC solver SPACER for basic sorts. Finally, the translation of that model into the formulas that suitably strengthen the postconditions of the given contracts. We will present our technique through an example consisting of a Scala program for reversing lists. Note that the Stainless verifier is not able to prove the correctness of that program when considering the given contracts, while it succeeds when considering the contracts with the strengthened postconditions constructed by applying our technique.

A machine learning method to variable classification in OpenMP

OpenMP is a parallel computing framework that provides programmers with a set of directives and clauses to use when writing parallel applications. The most important task in adopting OpenMP is deciding the parallel pattern with associated clauses to employ in a sequential program that already exists. The shared-memory parallelization is complicated by parallel directives with different roles. Some tools have been developed to assist programmers in developing parallel programs using OpenMP. Many tools, however, have constraints on the size of program analysis, OpenMP scoping, and scalar and array reduction. Manually selecting clauses with the necessary data-sharing attributes is also prone to errors. In this study, we target the variable classification in directives to explore the loop-level parallelism. We set the variable classification problem as a type inference task based on a machine learning method, which understands the attributes of variables in certain contexts and relations. We propose an aligned corpus of tokens and types to predict variable attributes used inside the target loop. We support the reduction clause whenever it is applicable. Experimental results indicate that our method is very promising and favorably suited to dealing with real-world complex programs while showing high accuracy.

Unprovability results for clause set cycles

The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we are able to characterize clause set cycles by a logical theory. We make use of this characterization to provide practically relevant unprovability results for clause set cycles that exploit different logical features.

Verifying Catamorphism-Based Contracts using Constrained Horn Clauses

AbstractWe 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.

Legal Analysis of Impact of Revised BIMCO Clauses on Crew Health and Safety During COVID-19 Era

This paper evaluates how the revised BIMCO Crew Change Clause 2020 affected crew health during this period. To satisfy the need for specific clauses, regulating the contractual relationships during the COVID-19 period, BIMCO created sets of clauses, such as the BIMCO Crew Change Clauses for Time Charter Parties (2020). The rationale of those clauses was based upon the pre-existing BIMCO Infectious or Contagious Diseases Clause for Voyage and Time Charter Parties 2015, but it was evidenced that the COVID-19 virus had many intricacies. Thus, new sets of rules are presently emerging to eliminate the gaps created. The basic downside of this legislation and the focus of this paper is to prove that these clauses are focused only on regulating the contractual relationship, without actually taking into consideration the crews’ health and safety.The analysis is focused on the impact of a COVID-19 incident on four specific legal aspects, i.e. i) vessels’ seaworthiness, ii) charter parties, iii) port safety, and iv) refusal of orders. There is also an analysis of the imminent Decease Clause 2021 and its actual impact upon the shipping industry. The analysis of the relevant legislation is based on legal doctrine, dominant form in legal research, aiming to provide a systematic exposition of the legal and regulatory principles. It analyzes the relationship between those principles to provide clarifications, utilizing legislation and relevant case law as the primary source of data. This research method is qualitative and is very similar to critical analysis, whose application is performed through (a) research and description of the existing legislation, (b) prescription, whose essence is to explore the statutory framework, locate the critical points, and assess the effectiveness of legislation on protecting the crew health and safety, and (c) evaluation of possible amendments or additions.The majority of studies conclude that shipping companies will be able to protect crew health and safety only through proactive measures and due diligence. The revised BIMCO terms on crew changes during Covid-19 and the new Disease Clause 2021 sadly did not have crew protection as their top priority. In most parts they tried to allocate and even mitigate the risk of the contracting parties, providing “windows” of opportunity for both sides to be excepted from any liability. Based on the analysis of resources, the new clause is not engaging the concept of proactive measures, unquestionably the most important method for the preservation of crew health usually referred to as “exercising due diligence”. It is a fact that BIMCO protects the clients’ interests, with the clients being the charter parties. It is also valid that the shipping industry supported the nations during the COVID-19 outbreak, but the BIMCO clauses were concentrated on the preservation of contractual relationships, leaving the concept of crew health and safety uncharted.

Model Checking Algorithm for Repairing Inference between Conjunctive Forms

Let K be a propositional formula and let ϕ be a query, the propositional inference problem K |= ϕ is a Co-NP-complete problem for propositional formulas without restrictions. We show the existence of polynomial-time cases for some fragments of propositional formulas K and ϕ that are different from the already known case of Horn formulas. For example, in the case that K is a formula in the fragment Krom or Horn or Monotone, then K |= ϕ can be decided in polynomial-time for any CNF ϕ. Given two conjunctive normal forms (CNF’s) K and ϕ, when K ̸|= ϕ, our proposal builds a minimal set of independent clauses S. The falsifying assignments of S are exactly the subset of models of K, which are not models for ϕ. In this way, the CNF S could extend the initial formula K in such a way that repair the inference, it is (S ∪ K) |= ϕ is held.

Optimal answer generation by equivalent transformation incorporating multi-objective genetic algorithm

This paper proposes a framework for time-efficiently finding multiple answers that meet multiple logical constraints and are Pareto-optimal for multiple objective functions. The proposed framework determines a set of optimal answers by iteratively replacing a set of definite clauses. Clause replacement is performed using a SAT solver consisting of equivalent transformation rules (ETRs). An ETR replaces a definite clause with one or more clauses while preserving the declarative meaning of the union of the original clause and problem clauses. To efficiently find optimal answers, in this paper, we define a new class of ETRs that are generated based on the evaluation results of a multi-objective genetic algorithm (MOGA) and propose a method for generating ETRs that belong to the new class. ETRs belonging to the new class help to replace definite clauses according to user objectives such as cost–benefit performance, reliability, and financial constraints. Thus, a SAT solver that uses the new ETR class in addition to extant ETR classes can preferentially replace definite clauses that produce the optimal answer for user objectives. Experimental results indicate that the proposed framework can significantly reduce the computation time and memory usage necessary to determine a set of optimal answers for user objectives.

Design Trade-Offs Under Power Asymmetry: COPs and Flexibility Clauses

Abstract Negotiating parties to an environmental agreement can manage uncertainty by including flexibility clauses, such as escape and withdrawal clauses. This article investigates a type of uncertainty so far overlooked by the literature: the uncertainty generated by the creation of a Conference of the Parties (COP) in a context of sharp power asymmetry. When negotiating an agreement, it is difficult for powerful states to make a credible commitment to weaker states, whereby they will not abuse their power to influence future COP decision-making. Flexibility clauses provide a solution to this credibility issue. They act as an insurance mechanism in case a powerful state hijacks the COP. Thus we expect that the creation of a collective body interacts with the degree of power asymmetry to make flexibility clauses more likely in environmental agreements. To test this argument, we draw on an original data set of several specific clauses in 2,090 environmental agreements, signed between 1945 and 2018. The results support our hypothesis and suggest that flexibility clauses are an important design feature of adaptive environmental agreements.

Satisfiability of constrained Horn clauses on algebraic data types: A transformation-based approach

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.

Numerical integration of overlap electron densities: Parallelization strategies for a good load balancing using OpenMP

Here we present a comprehensive assessment of how different OpenMP directives influence the computation speedup for the creation of the overlap electron density using linear combinations of atomic Gaussian-type orbitals. Also, we present the computational performance of a simple algorithm for numerical integration, based on the division of integration space in subspaces (with adaptive sizes considering its integral values - ASII). This algorithm is implemented and compared with the VEGAS algorithm with integrand parallelization. Here we present the performance comparison of 12 different sets of OpenMP directives and collapse clauses, and 15 different basis sets, that were tested for Br2 and H2O2 model systems. The OpenMP directives and clauses tests pointed to the schedule = dynamic or static, Nindex = 1, and collapse (2) clause as the best strategy for a load-balanced parallel computation. The ASII method presents speedup performance compared with a modern parallel implementation of the VEGAS algorithm. The best speedup obtained for the computation at a 64 core platform was ca. 48.0. A GitHub link with the built library and a simple example are also available.

A Fixed-point Theorem for Horn Formula Equations

We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn formula equations which is based on expressing the fixed-point computation of a minimal model of a set of Horn clauses on the object level as a formula in first-order logic with a least fixed point operator. We describe several corollaries of this fixed-point theorem, in particular concerning the logical foundations of program verification, and sketch how to generalise it to incorporate abstract interpretations.

Modelling and Verification Analysis of Cooperative and Non-Cooperative Games via a Modal Logic Approach

In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players (coalitions) due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be self-enforcing (e.g. through credible threats). Cooperative games are often analyzed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional non-cooperative game theory which focuses on predicting individual players’ actions and payoffs and analyzing Nash equilibriums. In this work, the cooperative and non-cooperative game problem is modeled by means of a modal logic formula. Then, using the concept of logic implication, and transforming this logical implication relation into a set of clauses, a modal resolution qualitative method for verification (satisfiability) as well as performance issues, for some queries is applied.

Stochastic Local Search over Minterms on Structured SAT Instances

We observed that Conjunctive Normal Form (CNF) encodings of structured SAT instances often have a set of consecutive clauses defined over a small number of Boolean variables. To exploit the pattern, we propose a transformation of CNF to an alternative representation, Conjunctive Minterm Canonical Form (CMCF). The transformation is a two-step process: CNF clauses are first partitioned into disjoint subsets such that each subset contains CNF clauses with shared Boolean variables. CNF clauses in each subset are then replaced by Minterm Canonical Form (i.e., partial solutions), which is found by enumeration. We show empirically that a simple Stochastic Local Search (SLS) solver based on CMCF can consistently achieve a higher success rate using fewer evaluations than the SLS solver WalkSAT on two representative classes of structured SAT problems.