This volume contains extended abstracts of the contributed talks presented at the FLoC Workshop on Proof Complexity held on July 7-8, 2018 in Oxford.

Proof complexity is the study of the complexity of theorem proving procedures. The central question in proof complexity is: given a theorem F (e.g. a propositional tautology) and a proof system P (i.e., a formalism usually comprised of axioms and rules), what is the size of the smallest proof of F in the system P? Moreover, how difficult is it to construct a small proof? Many ingenious techniques have been developed to try to answer these questions, which bare tight relations to intricate theoretical open problems from computational complexity (such as the celebrated P vs. NP problem), mathematical logic (e.g. separating theories of Bounded Arithmetic) as well as to practical problems in SAT and QBF solving.

The programme included 4 invited talks and 12 contributed papers, selected by the programme committee. The invited speakers were

• Christoph Berkholz, Humboldt University Berlin,
• Sam Buss, UCSD,
• Nicola Galesi, Sapienza University Rome, and
• Meena Mahajan, IMSc Chennai.

Topics presented at the workshop included recent and ongoing work on Proof Complexity, Bounded Arithmetic, Relations to SAT and QBF solving and to Computational Complexity. A novel feature of the workshop was the joint session with the FLoC Workshop Quantified Boolean Formulas and Beyond held on July 8. The joint session consisted of the invited talk of Meena Mahajan, four contributed talks, and a discussion.

The workshop was partly funded through an ESPRC Doctoral Prize Fellowship of Leroy Chew (University of Leeds). We thank the PC members, the organisers of FLoC, the presenters and all participants for making this workshop a success.