Using DAG transformations to verify Euler/Venn homogeneous and Euler/Venn FOL heterogeneous rules of inference

In this paper, we present a system that translates first order logic (FOL) formulas into natural language (NL) sentences. The motivation comes from an intelligent tutoring system teaching logic as a knowledge representation language, where it is used as a means for feedback to the users. FOL to NL conversion is achieved by using a rule-based approach, where we exploit the pattern matching capabilities of rules. So, the system consists of a rule-based component and a lexicon. The rule-based unit implements the conversion process, which is based on a linguistic analysis of a FOL sentence, and the lexicon provides lexical and grammatical information that helps in producing the NL sentences. The whole system is implemented in Jess, a java-based expert system shell. The conversion process currently covers a restricted set of FOL formulas.

Approximate pattern matching and transitive closure logics

The role of games in computing science has been given some consideration in the literature. We aim to design games that can be used for teaching logic. Specifically, we build on the Minefield game used in the Stanford Intro to Logic course, and present a version, which we call MineFOL, that incorporates time constraints. We also move beyond the Stanford examples in that we provide a formalisation of the game, with a view to eventually generating game instances automatically as well as from user input, and show how MineFOL can be used as a learning tool. We also developed an online platform supporting learners in at least three ways. First, the learners can practice reasoning in First Order Logic (FOL) and proving strategies such as resolution through various MineFOL games. Second, the learners can practice formalisation in FOL, by allowing learners to build their own games. Third, the learners become aware of the need of interleaving various technologies to solve a logicbased task. In this line, MineFOL is formalised in such way to allow augmenting reasoning in FOL with search strategies.

In this paper, a hierarchical ensemble classification approach that utilizes a Directed Acyclic Graph (DAG) structure is proposed as a solution to the multi-class classification problem. Two main DAG structures are considered: (i) rooted DAG, and (ii) non-rooted DAG. The main challenges that are considered in this paper are: (i) the successive misclassification issue associated with hierarchical classification, and (i) identification of the starting node within the non-rooted DAG approach. To address these issues the idea is to utilize Bayesian probability values to: select the best starting DAG node, and to dictate whether single or multiple paths should be followed within the DAG structure. The reported experimental results indicated that the proposed DAG structure is more effective than when using a simple binary tree structure for generating a hierarchical classification model.

BackgroundDirected acyclic graphs (DAGs) are an effective means of presenting expert-knowledge assumptions when selecting adjustment variables in epidemiology, whereas the change-in-estimate procedure is a common statistics-based approach. As DAGs imply specific empirical relationships which can be explored by the change-in-estimate procedure, it should be possible to combine the two approaches. This paper proposes such an approach which aims to produce well-adjusted estimates for a given research question, based on plausible DAGs consistent with the data at hand, combining prior knowledge and standard regression methods.MethodsBased on the relationships laid out in a DAG, researchers can predict how a collapsible estimator (e.g. risk ratio or risk difference) for an effect of interest should change when adjusted on different variable sets. Implied and observed patterns can then be compared to detect inconsistencies and so guide adjustment-variable selection.ResultsThe proposed approach involves i. drawing up a set of plausible background-knowledge DAGs; ii. starting with one of these DAGs as a working DAG, identifying a minimal variable set, S, sufficient to control for bias on the effect of interest; iii. estimating a collapsible estimator adjusted on S, then adjusted on S plus each variable not in S in turn (“add-one pattern”) and then adjusted on the variables in S minus each of these variables in turn (“minus-one pattern”); iv. checking the observed add-one and minus-one patterns against the pattern implied by the working DAG and the other prior DAGs; v. reviewing the DAGs, if needed; and vi. presenting the initial and all final DAGs with estimates.ConclusionThis approach to adjustment-variable selection combines background-knowledge and statistics-based approaches using methods already common in epidemiology and communicates assumptions and uncertainties in a standardized graphical format. It is probably best suited to areas where there is considerable background knowledge about plausible variable relationships. Researchers may use this approach as an additional tool for selecting adjustment variables when analyzing epidemiological data.

The Directed Acyclic Graph (DAG) is a graph representing causal pathways for informing the conduct of an observational study. The use of DAGs allows transparent communication of a causal model between researchers and can prevent over-adjustment biases when conducting causal inference, permitting greater confidence and transparency in reported causal estimates. In the era of ‘big data’ and increasing number of observational studies, the role of the DAG is becoming more important. Recent best-practice guidance for constructing a DAG with reference to the literature has been published in the ‘Evidence synthesis for constructing DAGs’ (ESC-DAG) protocol. We aimed to assess adherence to these principles for DAGs constructed within perioperative literature. Following registration on the International Prospective Register of Systematic Reviews (PROSPERO) and with adherence to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) reporting framework for systematic reviews, we searched the Excerpta Medica dataBASE (Embase), the Medical Literature Analysis and Retrieval System Online (MEDLINE) and Cochrane databases for perioperative observational research incorporating a DAG. Nineteen studies were included in the final synthesis. No studies demonstrated any evidence of following the mapping stage of the protocol. Fifteen (79%) fulfilled over half of the translation and integration one stages of the protocol. Adherence with one stage did not guarantee fulfilment of the other. Two studies (11%) undertook the integration two stage. Unmeasured variables were handled inconsistently between studies. Only three (16%) studies included unmeasured variables within their DAG and acknowledged their implication within the main text. Overall, DAGs that were constructed for use in perioperative observational literature did not consistently adhere to best practice, potentially limiting the benefits of subsequent causal inference. Further work should focus on exploring reasons for this deviation and increasing methodological transparency around DAG construction.

Rooted phylogenetic networks, or more generally, directed acyclic graphs (DAGs), are widely used to model species or gene relationships that traditional rooted trees cannot fully capture, especially in the presence of reticulate processes or horizontal gene transfers. Such networks or DAGs are typically inferred from observable data (e.g., genomic sequences of extant species), providing only an estimate of the true evolutionary history. However, these inferred DAGs are often complex and difficult to interpret. In particular, many contain vertices that do not serve as least common ancestors (LCAs) for any subset of the underlying genes or species, thus may lack direct support from the observable data. In contrast, LCA vertices are witnessed by historical traces justifying their existence and thus represent ancestral states substantiated by the data. To reduce unnecessary complexity and eliminate unsupported vertices, we aim to simplify a DAG to retain only LCA vertices while preserving essential evolutionary information. In this paper, we characterize LCA-relevant and lca-relevant DAGs, defined as those in which every vertex serves as an LCA (or unique LCA) for some subset of taxa. We introduce methods to identify LCAs in DAGs and efficiently transform any DAG into an LCA-relevant or lca-relevant one while preserving key structural properties of the original DAG or network. This transformation is achieved using a simple operator “⊖” that mimics vertex suppression.

We study Sowa’s conceptual graphs (CGs) with both existential and universal quantifiers. We explore in detail the existential fragment. We extend and modify Sowa’s original graph derivation system with new rules and prove the soundness and completeness theorem with respect to Sowa’s standard interpretation of CGs into first order logic (FOL). The proof is obtained by reducing the graph derivation to a question-answering problem. The graph derivation can be equivalently obtained by querying a Definite Horn Clauses program by a conjunction of positive atoms. Moreover, the proof provides an algorithm for graph derivation in a pure proof-theoretic fashion, namely by means of a slight enhancement of the standard PROLOG interpreter. The graph derivation can be rebuilt step-by-step and constructively from the resolution-based proof. We provide a notion of CGs in normal form (the table of the conceptual graph) and show that the PROLOG interpreter also gives a projection algorithm between normal CGs. The normal forms are obtained by extending the FOL language by witnesses (new constants) and extending the graph derivation system. By applying iteratively a set of rules the reduction process terminates with the normal form of a conceptual graph. We also show that graph derivation can be reduced to a question-answering problem in propositional datalog for a subclass of simple CGs. The embedding into propositional datalog makes the complexity of the derivation polynomial.

The expressiveness of First Order Logic (FOL) languages is severely counterbalanced by the complexity of matching formulas on a universe. Matching is an instance of the class of Constraint Satisfaction Problems (CSP), which have shown to undergo a phase transition with respect to two order parameters: constraint density and constraint tightness. This paper analyzes the problem of satisfying FOL Horn clauses in the light of these recent results. By means of an extensive experimental analysis, we show how Horn clause verification exhibits a typical phase transition with respect to the number of binary (or greater arity) predicates, and with respect to the ratio between the number of constants in the universe and the cardinality of the basic predicates extension.

Software Product Line (SPL) is a new methodology that develops software products by configuring a software product from artifacts repository. Variability is one of the important issues in designing SPL. It reflects the diversity and commonality of the artifacts in a product line. The success of SPL is basically dependent on model's variability. SPL contains three main issues: variability modeling, configuration of new software and the analysis of SPL. Validation is a vital operation among all these issues. In the literature, many methods of modeling variability are proposed but none of them focuses on the validation. In this paper, an intelligent method for validating SPL is introduced. The proposed method is based on two layers. The higher layer is a graphical representation (satisfying visualization condition), and the lower layer is logical representation of the variability using first order logic (FOL). The way that the proposed method can be used to model variability, and support the analysis and validation of SPL is described. Later a new operation in SPL validation issue is presented. Finally, the implementation of the two basic operations in the analysis of SPL is illustrated.

Directed acyclic graphs (DAGs) play a large role in the modern approach to causal inference. DAGs describe the relationship between measurements taken at various discrete times including the effect of interventions. The causal mechanisms, on the other hand, would naturally be assumed to be a continuous process operating over time in a cause–effect fashion. How does such immediate causation, that is causation occurring over very short time intervals, relate to DAGs constructed from discrete observations? We introduce a time-continuous model and simulate discrete observations in order to judge the relationship between the DAG and the immediate causal model. We find that there is no clear relationship; indeed the Bayesian network described by the DAG may not relate to the causal model. Typically, discrete observations of a process will obscure the conditional dependencies that are represented in the underlying mechanistic model of the process. It is therefore doubtful whether DAGs are always suited to describe causal relationships unless time is explicitly considered in the model. We relate the issues to mechanistic modeling by using the concept of local (in)dependence. An example using data from the Swiss HIV Cohort Study is presented.

Cancer progression models such as Oncogenetic Tress [1], Conjunctive Bayesian Networks [2], or CAPRI [3], try to infer possible restrictions in the order of accumulation of mutations using cancer cross-sectional data. These restrictions would arise from epistatic interactions between mutations. The Directed Acyclic Graphs (DAGs) returned by these methods predict the genotypes that can and cannot be observed. Since fitness landscapes are shaped by those same epistatics interactions and also specify what genotypes are accessible and inaccessible [4] we would expect a close correspondence between a fitness landscape and the DAGs inferred from evolutionary processes in that landscape. I will show here, however, that there is a many-to- many mapping between fitness landscapes and DAGs inferred from cancer progression models. I show that many fitness landscapes cannot be represented by a cancer progression DAG in the sense that no DAG can codify the genotypes that are accessible under that landscape and I propose two measures of “DAG-non-representability”. Next, using 500 different random fitness lanscapes (with 100 begin perfectly DAG-representable) I simulate cancer progression using different mutation rates and sampling regimes; I analyze 20 replicates (of 1000 genotypes) under each condition with CAPRI[3] and CBN[2]. I show that, even under constant mutation and sampling regime conditions, data obtained from the same landscape lead to inferring widely different DAGs (e.g., median Gini-Simpson index of 0.5); this one-landscape-to-many-DAGs phenomenon increases with DAG-non-representability. I also show the one-DAG-to-many-landscapes phenomenon where the same DAG is frequently inferred from very different fitness landscapes (e.g., > 50% difference in accessible genotypes). Finally, I “reverse landscape engineer” the pancreatic cancer data used in [6]: using 190 random fitness landscapes, I show that genotype frequencies similar to the empirically observed one can be obtained under fitness landscapes that are very different from each other and that produce data that lead to the inference of DAGs that are also widely different among themselves (e.g., pairwise difference in edges of DAGs > 50%). I discuss the implications of these results for the interpretation and applied use of cancer progression models. Novelty and significance This paper explicitly establishes a connection between the inference of cancer progression models and the fitness landscapes that condition that cancer progression. It shows there is a many-to- many mapping between them, even under large sample sizes, that can limit their interpretability.

Adjusting for Selection Effects in Epidemiologic Studies

Directed Gaussian graphical models with toric vanishing ideals

We propose a self-stabilizing algorithm to construct a minimal weakly $\mathcal{ST}$-reachable directed acyclic graph (DAG), which is suited for routing messages on wireless networks. Given an arbitrary, simple, connected, and undirected graph $G=(V, E)$ and two sets of nodes, senders $\mathcal{S} (\subset V)$ and targets $\mathcal{T} (\subset V)$, a directed subgraph $\vec{G}$ of $G$ is a weakly $\mathcal{ST}$-reachable DAG on $G$, if $\vec{G}$ is a DAG and every sender can reach at least one target, and every target is reachable from at least one sender in $\vec{G}$. We say that a weakly $\mathcal{ST}$-reachable DAG $\vec{G}$ on $G$ is minimal if any proper subgraph of $\vec{G}$ is no longer a weakly $\mathcal{ST}$-reachable DAG. This DAG is a relaxed version of the original (or strongly) $\mathcal{ST}$-reachable DAG, where every target is reachable from every sender. This is because a strongly $\mathcal{ST}$-reachable DAG $G$ does not always exist; some graph has no strongly $\mathcal{ST}$-reachable DAG even in the case $|\mathcal{S}|=|\mathcal{T}|=2$. On the other hand, the proposed algorithm always constructs a weakly $\mathcal{ST}$-reachable DAG for any $|\mathcal{S}|$ and $|\mathcal{T}|$. Furthermore, the proposed algorithm is self-stabilizing; even if the constructed DAG deviates from the reachability requirement by a breakdown or exhausting the battery of a node having an arc in the DAG, this algorithm automatically reconstructs the DAG to satisfy the requirement again. The convergence time of the algorithm is $O(D)$ asynchronous rounds, where $D$ is the diameter of a given graph. We conduct small simulations to evaluate the performance of the proposed algorithm. The simulation result indicates that its execution time decreases when the number of sender nodes or target nodes is large.