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Logic

Formal propositional calculus, truth-functional completeness, first-order predicate logic, and automated theorem proving engines.

1Propositional Calculus & Truth-Functional Operator Foundations

Inductive grammar of well-formed formulas, truth valuations, material implication paradoxes, and NAND gate completeness.

Truth Tables, Semantic Entailment & Sheffer Stroke Algebra

Formal definitions of propositional connectives and mathematical proof of single-operator functional completeness.

Propositional Connectives, Semantic Entailment & NAND Completeness

Inductive definition of well-formed formulas, 5 core logical truth functions, and Sheffer Stroke NAND reduction proofs.

2First-Order Predicate Logic, Quantification & Model Theory

Predicates, universal and existential quantifiers, Tarskian semantics, Prenex normal form, and Skolemization.

First-Order Structures, Quantified Semantics & Skolem Normal Form

Semantic structures, domain of discourse, interpretations, and syntactic elimination of existential quantifiers.

First-Order Predicate Logic, Model Theory & Robinson's Unification Algorithm

Master first-order predicate syntax, Tarskian model structures, Prenex normal form conversion, Skolemization, and Robinson's syntactic unification algorithm.

3Modal, Temporal & Non-Classical Logics for Distributed Systems

Kripke semantics, possible worlds accessibility relations, Linear Temporal Logic (LTL), and Computation Tree Logic (CTL).

Modal Kripke Semantics & Linear Temporal Logic (LTL) Verification

Accessibility relations in Kripke frames, temporal modal operators, and formal invariants in concurrent state spaces.

Kripke Semantics, Linear Temporal Logic (LTL) & Distributed Safety Invariants

Explore Kripke structures of possible worlds, modal operators of necessity and possibility, and Linear Temporal Logic (LTL) formulas for safety and liveness in concurrent systems.

4Satisfiability Modulo Theories (SMT), Hoare Logic & Formal Program Verification

Combining propositional SAT with background theory decision procedures (DPLL(T)), Nelson-Oppen congruence closure, and axiomatic Hoare triples.

SMT Solvers, DPLL(T) Architecture & Axiomatic Program Correctness

Nelson-Oppen equality sharing, uninterpreted functions, and loop invariant verification via weakest preconditions.

Satisfiability Modulo Theories (SMT), DPLL(T) & Hoare Logic Verification

Deconstruct the architecture of modern SMT solvers (Z3, CVC5), the DPLL(T) framework, Congruence Closure for uninterpreted functions, and Hoare Logic axiomatic verification.