Related papers: Proof Complexity of Substructural Logics
We present a streamlined and simplified exponential lower bound on the length of proofs in intuitionistic implicational logic, adapted to Gordeev and Haeusler's dag-like natural deduction.
The Strong Exponential Time Hypothesis (SETH) asserts that for every $\varepsilon>0$ there exists $k$ such that $k$-SAT requires time $(2-\varepsilon)^n$. The field of fine-grained complexity has leveraged SETH to prove quite tight…
We consider Proof Complexity in light of the unusual binary encoding of certain combinatorial principles. We contrast this Proof Complexity with the normal unary encoding in several refutation systems, based on Resolution and Integer Linear…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A length-bounded inference is of the form $prov(P,G,n)$ which…
Hitting formulas have been studied in many different contexts at least since [Iwama,89]. A hitting formula is a set of Boolean clauses such that any two of them cannot be simultaneously falsified. [Peitl,Szeider,05] conjectured that hitting…
We introduce proof nets for PiL, an extension of first-order multiplicative additive linear logic with new operators allowing a shallow encoding of processes in the {\pi}-calculus as formulas. We provide correctness criterion,…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically…
We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…
In this paper we explore the following question: how weak can a logic be for Rosser's essential undecidability result to be provable for a weak arithmetical theory? It is well known that Robinson's Q is essentially undecidable in…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…
Logic-based argumentation is a well-established formalism modelling nonmonotonic reasoning. It has been playing a major role in AI for decades, now. Informally, a set of formulas is the support for a given claim if it is consistent,…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field…
We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal…
This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…