MineFOL: a Game for Learning First Order Logic

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

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.

In this paper, we share our experiences concerning the introduction of the Android-based self-study app AXolotl within the first-semester logic course offered at our university. This course is mandatory for students majoring in Computer Science and Artificial Intelligence. AXolotl was used as part of an optional lab assignment bridging clausal reasoning and SAT solving with classical reasoning, proof construction, and first-order logic. The app provides an intuitive interface for proof construction in various logical calculi and aids the students through rule application. The goal of the lab assignment was to help students make a smoother transition from clausal and decompositional reasoning used earlier in the course to inferential and contextual reasoning required for proof construction and first-order logic. We observed that the lab had a positive influence on students' understanding and end the paper with a discussion of these results.

Software product Line (SPL) is an emerging methodology for developing software products. A successful software product is highly dependent on the validity of a SPL. Therefore, validation is a significant process within SPL. In this paper, inconsistency detection is investigated as operation for validating SPL. Intelligent rules are formulated detecting inconsistency based on deducing the results from predefined cases. First, variability is modeled using First Order Logic (FOL) predicates as a prerequisite for inconsistency detection. Later, inconsistency is categorized in three groups. For each group a general form is formulated that can coffer all possible cases. Finally, an intelligent rule (based on FOL) is illustrated for implementing each possibility. As results, all cases of inconsistency in the domain-engineering process are defined.

In this paper we will present a graph-transformation based method for the verification of heterogeneous first order logic (FOL) and Euler/Venn proofs. In previous work, it has been shown that a special collection of directed acyclic graphs (DAGs) can be used interchangeably with Euler/Venn diagrams in reasoning processes. Thus, proofs which include Euler/Venn diagrams can be thought of as proofs with DAGs where steps involving only Euler/Venn diagrams can be treated as particular DAG transformations. Here we will show how the characterization of these manipulations can be used to verify Euler/Venn proofs. Also, a method for verifying the use of heterogeneous Euler/Venn and FOL reasoning rules will be presented that is also based upon DAG transformations .

We outline a method for proving theorems in first-order logic with equality using some equational logics and their associated multiple-valued propositional logics, and describe an application of the method that makes use of the automated theorem-prover Otter to prove a range of theorems from the TPTP library of problems in first-order logic with equality.

Provenance is critical to the scientific integrity of archived data. It establishes the authenticity of science data by providing a detailed account of its origin, ownership, processing history, and any transformations that occurred over its lifecycle. In addition to validating authenticity, provenance facilitates the scientific evaluation of data and can be decisive in legal contexts regarding ownership and access.The Planetary Data System Information Model (PDS4 IM) provides some support for provenance such as limited processing history and source product identifiers.Nevertheless, the need for a more comprehensive and formalized approach to provenance tracking has been expressed across the PDS for derived data products, superseded unique identifiers, and the curation of data collections over time.To address these needs the W3C PROV Data Model (PROV-DM), Figure 1, has been adopted as the foundation for a robust, interoperable provenance model in PDS4.The PROV-DM Standard PROV-DM is a W3C Recommendation designed to support the interchange of provenance information on the Web. It introduces a generic yet expressive vocabulary for modeling entities, activities, and agents, as well as their interrelations such as wasDerivedFrom, wasGeneratedBy, wasAssociatedWith, and used. The adoption of PROV-DM in PDS4 provides a well-supported foundation for provenance interoperability. Figure 1 - PROV-DM: The W3C PROV Data ModelUsing GPT_4o, phase one consisted of the development of a general model aligned with PROV-DM and implemented as a PDS4 Local Data Dictionary (LDD), an extension to the PDS4 Information Model. As a general model, this LDD can in turn be specialized to support a diverse set of use cases across the PDS archive.Four use cases are currently under consideration. Each is conceptualized below by defining their PROV-DM entities and relationships.Voyager Corrected Image - This historical use case illustrates derivation of a corrected image from raw data and calibration files.Entities: CorrectedProduct, Raw Product, Calibration File Activities: Radiometric/Geometric Correction and Artifact Removal, Voyager Data Acquisition, Processing pipeline “vlev1” Agents: The software module components of “vlev1”, for example, findrx, remrx, and voycal. Relations: wasDerivedFrom, used, wasGeneratedBy, wasAttributedTo, wasAssociatedWith Superseded Logical Identifier (LID) - This use case tracks the relationship between a superseded identifier and a new identifierEntities: Superseded LID, New LID Activities: Superseding Activity Agents: PDS Discipline Node, data engineer Relations: wasDerivedFrom, wasAssociatedWith PDS Collection Stewardship – This use case describes the lifecycle of a collection across multiple versions and curatorial responsibility transfers.Entities: PDS Collection Version 1, PDS Collection Version 2 Activities: Archive, Management Agents: Discipline Node A, Discipline Node B Relations: wasGeneratedBy, wasAssociatedWith, used Planetary Science Observation – This use case captures the entities and relationships involved in a science observation.Investigation Goal: Volatile Mapping on Ryugu Spacecraft: Hayabusa2 (operated by JAXA) Instruments: Near-Infrared Spectrometer (NIRS3), Thermal Infrared Imager (TIR) Activity: Observation Campaign 1 Entities: Digital objects (e.g., spectra, images, thermographs) Targets: Crater A, Boulder Cluster B, Equatorial Ridge, Polar Region, Landing Site Z Relations: wasDerivedFrom, wasGeneratedBy, used, wasAssociatedWith, wasInformedBy A pseudo-XML representation representing some of the entities, activities, agents, and relationships for the first use case is provided below. Voyager Corrected Image Derived From EDR Image The VoyagerISSCorrectedImage was derived from the EDRImage. entity_voyager_corrected_image entity_voyager_edr_image activity_data_correction Some challenges remain in finalizing the implementation strategy:Identify and define the possible reasons for identifier supersession: Superseded, Replaced, Error, etc. Determine the suitability and granularity of W3C PROV relationships for the PDS. Determine appropriate use of bidirectional vs. unidirectional references between data products. Develop policies and procedures for governance to ensure consistent provenance recording and utilization. Conclusion The application of the W3C PROV-DM standard to the PDS4 information model represents a significant step toward improving the traceability, interoperability, and scientific trustworthiness of planetary data. The use cases presented demonstrate a broad applicability across contexts, from spacecraft imaging pipelines to multi-node stewardship models. Continued refinement of relationship types and implementation strategies will ensure alignment with both scientific practice and digital preservation principles.References W3C. (2013). PROV-DM: The PROV Data Model. https://www.w3.org/TR/prov-dm/AcknowledgementsThe research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.During the preparation of this work the author(s) used GPT4o in order to transform natural language to First Order Logic (FOL) and then to several Data Definition Languages (DDL). After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the publication.© 2025 California Institute of Technology. Government sponsorship acknowledged.

Modern software applications store their data in remote cloud servers. Users interact with these applications using web browsers or thin clients running on mobile devices. A key concern for these applications is the correctness of the actions that update the data store, which are triggered by user requests. Considering that modern applications store and manage data for millions (even billions) of users, misuse or loss of user data can have catastrophic consequences. In this paper, we focus on automated discovery of data store bugs in applications that use development frameworks that are RESTful, enforce the Model–View–Controller architecture, and use Object Relational Mapping libraries to manipulate data. We present a formal data model for data stores and data store manipulation in such applications. We have developed a framework for verification of data models via translation to First Order Logic (FOL), followed by automated theorem proving. Due to the undecidability of FOL, this automated approach does not always produce a conclusive answer. We investigate the use of many-sorted logic in data model verification in order to improve the effectiveness of this approach. Many-sorted logic allows us to specify type information explicitly, thus lightening the burden of reasoning about type information during theorem proving. Our experimental results demonstrate that our verification approach is scalable to real-world web applications and is able to detect bugs in them.

In spite of the amazing results obtained by deep learning in many applications, a real intelligent behavior of an agent acting in a complex environment is likely to require some kind of higher-level symbolic inference. Therefore, there is a clear need for the definition of a general and tight integration between low-level tasks, processing sensorial data that can be effectively elaborated using deep learning techniques, and the logic reasoning that allows humans to take decisions in complex environments. This paper presents LYRICS, a generic interface layer for AI, which is implemented in TensorFlow (TF). LYRICS provides an input language that allows to define arbitrary First Order Logic (FOL) background knowledge. The predicates and functions of the FOL knowledge can be bound to any TF computational graph, and the formulas are converted into a set of real-valued constraints, which participate to the overall optimization problem. This allows to learn the weights of the learners, under the constraints imposed by the prior knowledge. The framework is extremely general as it imposes no restrictions in terms of which models or knowledge can be integrated. In this paper, we show the generality of the approach showing some use cases of the presented language, including model checking, supervised learning and collective classification.

Concept Formation is a unsupervised learning task usually decomposed into the two subtasks of clustering and characterization. This paper presents a novel approach to Concept Formation in First Order Logic (FOL) which adopts a pattern-based approach to clustering and a bias-based approach to characterization. The resulting method extends therefore the levelwise search method for Frequent Pattern Discovery. The FOL fragment chosen is \(\mathcal{AL}\)-log, a hybrid language that merges the description logic \(\mathcal{ALC}\) and the clausal logic Datalog and turns out to be suitable for applications in the context of Ontology Refinement. Indeed the method returns a taxonomy rooted into the concept that occurs in an existing taxonomic ontology and needs to be refined in the light of new knowledge coming from an external data source. Experimental results have been obtained on an \(\mathcal{ALC}\) ontology enriched with Datalog data extracted from the on-line CIA World Fact Book.

In the domain of ontology design as well as in Conceptual Modeling, representing part-whole relations is a long-standing challenging problem. However, in most papers the focus has been on properties of the part-whole relation, rather than on its semantics. In the last decades, most approaches which have addressed the formal specification of the part-whole relation (i) rely on First Order Logic (FOL) which is unable to address multiple levels of granularity and (ii) do not support any typing mechanism useful for the extensional side of concepts and then, many difficulties remain especially about expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but so far, they have not been applied in the formalization of ontological relations. To bridge this gap, we present an axiomatization of the part-whole relation which hold between typed terms. Relation structures in the dependently-typed framework rely on a constructive logic. We define in a precise way what relation structures and their meta-properties, are in term of type classes using the Coq language.

On Expressive Completeness of Duration and Mean Value Calculi (Extended Abstract)