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The Abella interactive theorem prover is based on an intuitionistic logic that allows for inductive and co-inductive reasoning over relations. Abella supports the λ-tree approach to treating syntax containing binders: it allows simply typed λ-terms to be used to represent such syntax and it provides higher-order (pattern) unification, the ∇ quantifier, and(More)
The sequent calculus admits many proofs of the same conclusion that differ only by trivial permutations of inference rules. In order to eliminate this " bureaucracy " from sequent proofs, deductive formalisms such as proof nets or natural deduction are usually used instead of the sequent calculus, for they identify proofs more abstractly and geometrically.(More)
Forward reasoning in the propositional fragment We shall now begin our investigation into the use of the sequent calculus for automated reasoning in various fragments of linear logic. The first fragment we pick is the proposi-can be readily extended to include possibility. We begin by examining the problem of resource non-determinism in the backward(More)
1 Overview TLAPS, the TLA + proof system, is a platform for the development and mechanical verification of TLA + proofs. The TLA + proof language is declarative, and understanding proofs requires little background beyond elementary mathematics. The language supports hierarchical and non-linear proof construction and verification, and it is independent of(More)
It is standard to regard the intuitionistic restriction of a classical logic as increasing the expressivity of the logic because the classical logic can be adequately represented in the intuitionistic logic by double-negation, while the other direction has no truth-preserving propositional encodings. We show here that subexponential logic, which is a family(More)
The logic of hereditary Harrop formulas (HH) has proven useful for specifying a wide range of formal systems that are commonly presented via syntax-directed rules that make use of contexts and side-conditions. The two-level logic approach, as implemented in the Abella theorem prover, embeds the HH specification logic within a rich reasoning logic that(More)
For λ-terms constructed freely from a type signature in a type theory such as LF, there is a simple inductive subordination relation that is used to control type-formation. There is a related – but not precisely complementary – notion of independence that asserts that the inhabitants of the function space τ 1 → τ 2 depend vacuously on their arguments.(More)
Subexponential logic is a variant of linear logic with a family of exponential connectives—called subexponentials—that are indexed and arranged in a pre-order. Each subexponential has or lacks associated structural properties of weakening and contraction. We show that classical propositional multiplicative linear logic extended with one unrestricted and two(More)
The inverse method is a generalization of resolution that can be applied to non-classical logics. We have recently shown how Andreoli’s focusing strategy can be adapted for the inverse method in linear logic. In this paper we introduce the notion of focusing bias for atoms and show that it gives rise to forward and backward chaining, generalizing both(More)