Basics and Concepts of First-Order Theorem Proving
An accessible introduction to the fundamentals of first-order theorem proving, covering syntax, semantics, proofs, and the core concepts behind automated reasoning.
Formal Systems
Abductive Reasoning: Hypothesis Generation and Inference
Comprehensive guide to abductive reasoning, exploring how to generate and evaluate hypotheses that explain observations.
Answer Set Programming: Logic Programming with Stable Models
Comprehensive guide to answer set programming, exploring logic programming with stable model semantics for knowledge representation and reasoning.
Automated Reasoning in Software Engineering: Verification and Testing
Comprehensive guide to automated reasoning applications in software engineering, exploring verification, testing, and quality assurance.
Automated Theorem Proving: Overview and Foundations
Comprehensive introduction to automated theorem proving, exploring how to automatically discover and verify mathematical proofs using computational methods.
Axiomatic Semantics: Proving Program Properties
Comprehensive guide to axiomatic semantics, exploring how to prove program correctness using Hoare logic, preconditions, postconditions, and invariants.
Backtracking and Search Algorithms: Systematic Problem Solving
Comprehensive guide to backtracking and search algorithms, exploring systematic approaches to solving constraint and optimization problems.
Boolean Satisfiability (SAT) Problem: Computational Complexity
Comprehensive guide to the Boolean satisfiability problem, exploring NP-completeness, practical algorithms, and applications in automated reasoning.
Combinational Logic Design: Building Complex Circuits
Comprehensive guide to combinational logic design, exploring systematic approaches to designing complex circuits from specifications to implementation.
Constraint Logic Programming: Combining Logic and Constraints
Comprehensive guide to constraint logic programming, exploring how to combine logic programming with constraint solving for powerful problem-solving.
Constraint Propagation Techniques: Reducing Search Space
Comprehensive guide to constraint propagation techniques, exploring how to efficiently reduce search space in constraint satisfaction problems.
Constraint Satisfaction Problems: Solving Complex Constraints
Comprehensive guide to constraint satisfaction problems, exploring how to solve complex constraint systems using propagation and search techniques.
Denotational Semantics: Mathematical Meaning of Programs
Comprehensive guide to denotational semantics, exploring how to assign mathematical meanings to programs and language constructs using domain theory and fixed-point theory.
Description Logics and Ontologies: Formal Knowledge Representation
Comprehensive guide to description logics and ontologies, exploring formal approaches to knowledge representation with decidable reasoning.
Formal Verification Overview: Ensuring System Correctness
Comprehensive overview of formal verification, exploring techniques for proving that systems satisfy their specifications.
Fuzzy Logic and Approximate Reasoning: Handling Uncertainty
Comprehensive guide to fuzzy logic and approximate reasoning, exploring how to handle vagueness and uncertainty in reasoning systems.
Hybrid Reasoning Systems: Combining Multiple Approaches
Comprehensive guide to hybrid reasoning systems, exploring how to combine logical reasoning with machine learning and other approaches.
Interactive Theorem Provers: Coq, Isabelle, and Beyond
Comprehensive guide to interactive theorem provers, exploring how to use tools like Coq and Isabelle for formal verification and mathematical proof.
Karnaugh Maps: Simplifying Boolean Functions
Comprehensive guide to Karnaugh maps, exploring how to visually simplify Boolean functions for efficient circuit design and logic optimization.
Knowledge Graphs for AI: Structured Knowledge at Scale
Comprehensive guide to knowledge graphs, exploring how to build and reason over large-scale structured knowledge for AI applications.
Knowledge Representation Fundamentals: Encoding Knowledge
Comprehensive guide to knowledge representation, exploring how to formally encode knowledge for automated reasoning and AI systems.
Logic Gates and Circuits: Building Digital Systems
Comprehensive guide to logic gates and circuits, exploring how to build digital systems from basic gates, circuit analysis, and practical implementation.
Logical AI and Symbolic Reasoning: Foundations of Intelligent Systems
Comprehensive guide to logical AI and symbolic reasoning, exploring how formal logic enables intelligent systems to reason about the world.
Logical Reasoning in Cybersecurity: Threat Analysis and Defense
Comprehensive guide to logical reasoning applications in cybersecurity, exploring threat analysis, security verification, and automated defense.
Löwenheim-Skolem Theorem: Cardinality and Model Existence
Comprehensive guide to the Löwenheim-Skolem theorem, exploring how first-order logic relates to model cardinality, infinite models, and the limitations of first-order expressiveness.
Model Checking Basics: Automated Verification of Systems
Comprehensive introduction to model checking, exploring how to automatically verify that systems satisfy formal specifications using state-space exploration and temporal logic.
Modern SAT/SMT Techniques: Advanced Solving Methods
Comprehensive guide to modern SAT/SMT techniques, exploring advanced methods that make solvers practical for industrial applications.
Natural Deduction Systems: Intuitive Proof Methods
Comprehensive guide to natural deduction systems, exploring intuitive proof methods that mirror human reasoning patterns.
Non-Monotonic Reasoning: Reasoning with Incomplete Information
Comprehensive guide to non-monotonic reasoning, exploring how to reason effectively with incomplete and uncertain information.
Operational Semantics: Execution and Computation Models
Comprehensive guide to operational semantics, exploring how to formally specify program execution through transition systems, evaluation rules, and computation models.
Prolog: Fundamentals and Programming
Comprehensive guide to Prolog programming, exploring logic programming fundamentals and practical Prolog development.
Proof Assistants and Formal Verification: Ensuring Correctness
Comprehensive guide to proof assistants and formal verification, exploring how to ensure correctness of software and hardware systems.
Reasoning Systems and Inference Engines: Automated Deduction
Comprehensive guide to reasoning systems and inference engines, exploring how to build systems that automatically derive conclusions from knowledge bases.
Resolution and Refutation: Proof by Contradiction
Comprehensive guide to resolution and refutation, exploring how to prove theorems by deriving contradictions from negated goals.
SAT Solvers: Modern Algorithms and Techniques
Comprehensive guide to modern SAT solver algorithms, exploring CDCL, heuristics, and techniques that make SAT solvers practical for real-world problems.
Satisfiability Modulo Theories (SMT): Beyond Boolean Logic
Comprehensive guide to satisfiability modulo theories, exploring how to solve problems in theories like arithmetic, arrays, and uninterpreted functions.
Semantic Equivalence: Comparing Program Meanings
Comprehensive guide to semantic equivalence, exploring how to determine when two programs have the same meaning, including bisimulation, observational equivalence, and equivalence checking.
Semantic Networks and Frames: Structured Knowledge Representation
Comprehensive guide to semantic networks and frames, exploring structured approaches to knowledge representation for AI systems.
Sequent Calculus: Symmetric Proof Systems
Comprehensive guide to sequent calculus, exploring symmetric proof systems with structural rules and their applications in automated reasoning.
Sequential Logic and State Machines: Adding Memory to Circuits
Comprehensive guide to sequential logic and state machines, exploring how to design circuits with memory, state transitions, and complex behaviors.
Tableau Methods: Systematic Proof Search
Comprehensive guide to tableau methods, exploring systematic proof search through semantic tableaux and their applications in automated reasoning.
Temporal Logic: Reasoning About Time and Change
Comprehensive guide to temporal logic, exploring how to formally specify and verify properties that change over time.