Module description
The module offers a comprehensive study of the fundamental meta-theoretic properties of predicate logic that are necessary prerequisites for advanced logical theorising. The main aim of the module is to provide a detailed proof of the Adequacy theorem for predicate logic: A suitable deductive system for predicate logic will be shown to be sound (all proofs correspond to valid arguments) and complete (valid arguments do not exceed whats provable).
Additional properties of predicate logic such as the ones described by the Compactness and the Löwenheim-Skolem theorems will be presented and discussed. In the light of such properties, predicate logic will be compared to other philosophically relevant logical systems - such as higher-order logics - for which the Adequacy theorem fails.
Assessment details
When this module is taught in the Autumn term (Semester 1), there will be alternative assessment for Study Abroad students at King's for Semester 1 only.
FULL YEAR Study Abroad students:
Summative assessment: Problem sets, 1 hour (30%); Unseen written exam, 2 hours (70%).
SEMESTER 1-ONLY Study Abroad students:
Summative assessment: Problem sets, 1 hour (30%); Unseen written exam, 2 hours (70%) in DECEMBER.
Formative assessment: NONE
Educational aims & objectives
- To provide a meta-theoretic approach to the semantics and proof-theory of predicate logic as opposed to the internal perspective proper of elementary introductions to logic.
- To present the fundamental meta-theoretic properties of predicate logic as captured by the soudness and completeness theorems.
- To introduce some immediate but crucial consequences of the soudness and completeness theorem: the compactness and the Löwenheim-Skolemtheorems.
- To compare predicate logic with other philosophically relevant logical systems, such as higher-order logic, for which completeness, compactness,and Löwenheim-Skolem fail.
Learning outcomes
By the end of the module, students will be able to demonstrate intellectual, transferable, and practical skills appropriate to a Level 5 module and in particular will be able to demonstrate:
- a deep understanding of the semantic notions of truth, satisfaction, and logical consequence for predicate logic, and of different but equivalent proof-theoretic calculi (natural deduction, Hilbert systems, sequent calculi)
- a detailed knowledge of the soudness of natural deduction rules with respect to first-order models;an understanding of the fundamental steps of the proof of the completeness of predicate logic
- a critical acquaintance with what distinguishes first and higher-order logics and with the philosophical significance of such distinction.
Teaching pattern
One one-hour weekly lecture and one one-hour weekly seminar over ten weeks.