first_order_logic_inference_____2047.pptx

first_order_logic_inference

1. ANNASAHEB DANGE COLLEGE OF ENGINEERING AND TECHNOLOGY (An Empowered autonomous Institute) ARTIFICIAL INTELLIGENCE AND DATA SCIENCE First Order Logic Inference Under The Course “1ADPC204”/ Foundations Of Artificial Intelligence Academic Year-2025-2026 Presented By:-Ayaz Ahmad Class:-S.Y. B.Tech Branch:-AI&DS Under The Guidance of:-Prof. Krishnakumar

2. Contents Objectives Introduction Meaning/Definition of FOL Inference Principles of FOL Inference Importance FOL Inference Essential Characteristics of FOL Inference Types of FOL Inference Field FOL Inference Pillars of FOL Inference Feature / Future of FOL Inference Benefits of Ethics / Challenges of Ethics FOL Applications FOL Inference Outcomes Reference

3. Objective Formal representation of knowledge First-Order Logic (FOL) allows the representation of knowledge about objects, properties, and relationships in a structured manner. By using formal symbols, we model real-world scenarios with clarity and consistency. Weave relatable stories into your presentation using narratives that make your message memorable and impactful Deriving new information with inference rules FOL inference enables the derivation of new conclusions from existing facts and rules. Using systems like modus ponens or resolution, machines expand their knowledge base step by step, ensuring validity. Application in problem-solving across domains Logical reasoning is central to fields like natural language processing, expert systems, robotics, and theorem proving. FOL helps systems make decisions and solve problems by applying formalized rules and facts. Evaluation of reasoning mechanisms An essential part of studying FOL is ensuring reasoning is correct, sound, and complete. Correctness guarantees conclusions are valid, soundness ensures they’re true, and completeness ensures all valid conclusions are derived. Bridging human reasoning and automated decision-making FOL bridges human-like reasoning and automated systems. Through formal semantics, machines can mimic human thought, enabling decision-making that aligns with logical structures humans use.

4. Introduction First-Order Logic (FOL) is one of the most expressive and widely used knowledge representation frameworks in artificial intelligence. It extends propositional logic by introducing predicates , variables , and quantifiers , allowing the expression of relationships between objects and general rules that apply to multiple entities. Inference in FOL refers to the process of deriving logically valid conclusions from a set of premises using sound reasoning rules . This capability is crucial in AI systems that must make decisions or predictions based on incomplete or implicit information. Example: Premise 1: ∀x (Human(x) → Mortal(x)) Premise 2: Human(Socrates) Conclusion (via inference): Mortal(Socrates) Why FOL Inference is important in AI: It provides a foundation for automated reasoning . It enables AI to work with abstract concepts and generalizations rather than just specific facts. It is domain-independent and applicable to any area where logical reasoning is needed.

5. Meaning of FOL Inference Definition and Purpose of FOL Inference First-Order Logic (FOL) inference is the process of deriving new conclusions from a set of known facts and rules using valid reasoning techniques like Modus Ponens, Resolution, or Unification. It ensures that if the premises are true, the derived conclusions are also true. Logical Entailment and Soundness Inference in FOL guarantees that derived statements are logically entailed by the original knowledge base (KB), preserving truth. This means if KB ⊨ α, then α is true in all models where KB is true, ensuring sound reasoning. Inference Techniques Common methods for FOL inference include forward chaining, backward chaining, and resolution. These techniques apply inference rules systematically to derive valid conclusions from the KB. Applications and Importance FOL inference is foundational in fields like automated theorem proving, logic programming, and AI reasoning systems. It provides a formal basis for machines to perform logical decision-making and reasoning.

6. Principles of FOL Inference FOL inference ensures soundness by deriving only logically valid conclusions and completeness by being capable of deriving all conclusions entailed by the knowledge base. The knowledge base must be logically consistent, as any contradictions can lead to the inference of arbitrary conclusions, making the system unreliable due to the principle of explosion. Unification aligns predicates with similar structures, while substitution replaces variables with constants or terms to enable proper matching during the inference process. Inference relies on applying formal rules such as Modus Ponens, Resolution, Universal Instantiation, and Existential Instantiation to derive new sentences from existing ones.

7. Principles of FOL Inference

8. Importance FOL Inference Importance Of FOL Enables machines to perform logical reasoning by deriving new knowledge from existing facts and rules expressed in formal logic. Provides a structured and precise way to represent complex relationships, properties, and entities in various domains. Forms the foundation for advanced applications like automated theorem proving, expert systems, and AI reasoning engines. Ensures the reliability of conclusions through soundness and completeness, allowing trustworthy decision-making. Bridges the gap between human logical thinking and machine-based reasoning by using formal semantics and inference rules. Supports various inference techniques like forward chaining, backward chaining, and resolution, which are essential for problem-solving in AI and computer science.

9. Characteristics of FOL Inference

10. Types of FOL Inference

11. Types of FOL Inference

12. Scope Of FOL Inference

13. Pillars of First-Order Logic Inference

14. Pillars of First-Order Logic Inference

15. Future of First-Order Logic Inference

16. Future of First-Order Logic Inference

17. Challenges of FOL Inference 1. Complexity and Computational Cost: FOL inference can be computationally expensive because it involves searching through many possible substitutions and combinations of variables. As the number of facts and rules grows, reasoning can become slow and resource-intensive. 2. Ambiguity in Natural Language: Human language is often ambiguous and context-dependent, making it hard to map it directly into logical rules without losing meaning or introducing errors. Example: The sentence “John saw the man with the telescope” can be interpreted in multiple ways, but FOL inference requires a precise logical representation to reason correctly.

18. Challenges of FOL Inference 3. Difficulty Representing Probabilistic Knowledge: FOL inference is deterministic—it either proves or disproves something based on the rules and facts. It struggles to incorporate probabilities or degrees of belief.   4. Scalability Issues: As the number of entities, relationships, and rules increases, FOL inference systems may not scale efficiently, leading to performance bottlenecks.

19. Applications FOL Inference

20. Applications FOL Inference Automated Theorem Proving : FOL inference is widely used in proving mathematical and logical statements by applying axioms and deduction rules. It reduces manual effort in domains like mathematics and engineering. Example: Proving that the sum of angles in triangle ABC is 180° based on geometric rules. 2) Logic Programming (e.g., Prolog ) : Languages like Prolog use FOL inference to answer queries by matching facts and rules, enabling reasoning over relationships. Example: From parent(John, Mary) and the rule “A parent is an ancestor,” the system infers ancestor(John, Mary). 3) Natural Language Processing (NLP): FOL helps represent sentence meanings in logic, allowing systems to reason about language, relationships, and implications. Example: From “Every student who studies passes,” it infers “If Alice studies, she will pass.” 4) Expert Systems: Expert systems apply FOL inference to mimic human reasoning in areas like medicine or finance, providing consistent decisions. Example: Inferring that “fever + cough → flu” supports faster medical diagnosis.

21. Applications FOL Inference 5) Robotics and Autonomous Systems Robots use FOL inference to reason over rules and sensor data, enabling safe navigation and decision-making. Example: A robot follows “If obstacle detected, turn left” to avoid collisions. 6) Semantic Web and Knowledge Graphs FOL inference links entities across datasets, enhancing intelligent search and recommendations. Example: Inferring company relationships by shared location and industry. 7) Formal Verification and Safety-Critical Systems Used to verify system correctness and safety in critical domains like aerospace or transport. Example: Inferring “If all checks passed, aircraft is safe to fly.”

22. Applications FOL Inference

23. Outcome Enhanced Understanding of Logical Reasoning Methods The study developed a strong foundation in various inference techniques of First-Order Logic, such as forward chaining, backward chaining, and resolution. These methods enable systematic reasoning and form the backbone of intelligent decision-making in AI. Ability to Model Real-World Problems Formally Learners gained the capability to represent real-world scenarios in a structured, machine-readable format using predicates, quantifiers, and logical rules. This outcome demonstrates the practical application of FOL inference in building intelligent systems. Awareness of Theoretical and Practical Limitations The report emphasized the computational challenges of FOL inference, such as decidability, semi-decidability, and complexity issues. Understanding these limitations prepares learners to design efficient reasoning systems while being aware of scalability concerns. Recognition of Ethical Responsibilities in AI Systems The outcomes highlight the importance of considering ethics when applying FOL inference. Students recognized the need for transparency, fairness, and accountability in logical reasoning systems to ensure trustworthiness in real-world applications.

24. References Textbooks: Artificial Intelligence: A Modern Approach — Russell & Norvig Logic in Computer Science — Huth & Ryan Artificial Intelligence: Foundations of Computational Agents — Alan Mackworth & David L. Poole Online Links: TutorialsPoint – Inference Rules in FOL Johns Hopkins CS Lecture Slides (Inference in FOL) Tutorial for Beginners – Inference in FOL Wikipedia – First-order logic Other Resourses : Artificial Intelligence: A New Synthesis — Nilsson IEEE Xplore and ACM Digital Library

25. Conclusions Core of AI Reasoning – FOL inference provides a formal way for machines to reason logically using facts, rules, and relationships. It forms the foundation of intelligent decision-making. Wide Applications – It is applied in expert systems, natural language processing, robotics, automated theorem proving, and safety-critical systems, showing its versatility across domains. High Expressiveness – FOL can represent complex knowledge using predicates, quantifiers, and logical connectives, making it more powerful than propositional logic. Key Challenges – Despite its strengths, it faces issues like computational complexity, scalability problems, and limitations in handling uncertainty or probabilistic reasoning. Future Importance – With proper optimization and integration with modern AI techniques, FOL inference will remain vital in developing intelligent, transparent, and trustworthy AI systems.

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