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Agenda 2/24/26

  1. Assignments
  2. Future schedule
  3. QL Predicate Trees

Assignments

  1. Due: QL Proofs Quizzes
  2. Due: Syllabus Construction Assignment
  3. Due: Assignment Construction Assignment

Future Schedule

  • March 3: Ch. 8 - Predicate Logic Proofs.
  • March 17: Ch. 9.1-9.3 - Beyond Propositional Logic: Extending and Deviating from Classical Logic, Truth-functional completeness, Peirce Arrow and Sheffer Stroke, Prefix and postfix notation, Existential Graphs
  • March 24: Ch. 9.4 - Reasons for rejecting bivalence and Multi-valued logics: Bochvar, Lukasiewicz, Kleene, Supervaluationism, Definitely
  • March 31: Ch. 12.1-12.2 - Proof Styles: Jaskowski, Fitch, Lemmon-Suppes, Sequent, Existential Graphs (alpha), Axiomatic
  • April 7: Variable Assignments, Identity, Definite Descriptions, and Lambda abstraction
  • April 14: Modal Propositional Logic
  • April 21: ?
  • April 28: Presentations

Topics:

  1. Relevance logic: deviant logic that requires antecedent and consequent of conditional to be "relevantly related"
  2. Informal logic (Critical Thinking): branch of logic that focuses on identifying, analyzing, and evaluating arguments in everyday language, e.g., fallacies.
  3. Feminist logic: no universal definition but generally a philosophical inquiry to whether either (1) logic is value-free, (2) logic promotes masculine (misogynistic) ends, or (3) whether there is a particular kind of logic that promotes feministic goals.
  4. Metaphysics and Logic: Many metaphysical ideas are expressed using logical concepts, e.g., supervenience, contemporary ontological arguments, causation are expressed using modal notions, the relation between qualitative and numerical identity (Leibniz's laws) is expressed using second-order predicate logic, the non-existence of vague objects using identity and lambda-abstreaction, "exists" using predicate logic.
  5. Free logic: in classical logic, names have existential import and the domain of discourse is non-empty. In free logic, we drop these assumptions.
  6. Experiments in logic: what empirical studies are there on the ability of human beings to reason formally?

QL Predicate Trees

Tree Rules

QL adds four new tree rules:

  1. Negated Existential Decomposition
  2. Negated Universal Decomposition,
  3. Existential Decomposition,
  4. Universal Decomposition

Completed Open Branches

There is an important distinction between a PL Open Branch and a QL Open Branch.

Limitations

  • PL is decidable. You can use the table / tree method to determine if a wff is a tautology or an argument is valid.
  • QL is proven to be undecidable. There is no general method / algorithm that can determine all QL tautologies.
  • QL is, however, semidecidable. The tree method can show that a wff is a tautology, but sometimes the tree method will run forever.
  • Some fragments of QL are decidable, e.g., monadic predicate logic using only 1-place predicates.