Related papers: Interpolation in Proof Theory
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
We address the problem of reasoning about interleavings in safety verification of concurrent programs. In the literature, there are two prominent techniques for pruning the search space. First, there are well-investigated trace-based…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
Resolution and superposition are common techniques which have seen widespread use with propositional and first-order logic in modern theorem provers. In these cases, resolution proof production is a key feature of such tools; however, the…
The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given.
Which choices of truth tables and consequence relations for two logics $\mathsf{L}_1$ and $\mathsf{L}_2$ ensure the satisfaction of the following split interpolation property: If two formulas $\phi$ and $\psi$ share at least one…
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and…
System I is a proof language for a fragment of propositional logic where isomorphic propositions, such as $A\wedge B$ and $B\wedge A$, or $A\Rightarrow(B\wedge C)$ and $(A\Rightarrow B)\wedge(A\Rightarrow C)$ are made equal. System I enjoys…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
We prove normalization for MTT, a general multimodal dependent type theory capable of expressing modal type theories for guarded recursion, internalized parametricity, and various other prototypical modal situations. We prove that deciding…
Using polyadic MV algebras, we show that many predicate many valued logics have the interpolation property.
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…
TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…
In this paper, we study several propositional team logics that are closed under unions, including propositional inclusion logic. We prove that all these logics are expressively complete, and we introduce sound and complete systems of…
We show how Pick interpolation and interpolation on peak interpolation sets can be combined in an abstract uniform algebra setting. In particular as a special case, the Rudin-Carleson theorem can be combined with the classical Pick…
We propose a methodology for verifying security properties of network protocols at design level. It can be separated in two main parts: context and requirements analysis and informal verification; and formal representation and procedural…
The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main…
An important component of a number of computational modeling algorithms is an interpolation method that preserves the positivity of the function being interpolated. This report describes the numerical testing of a new positivity-preserving…