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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)

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 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)

We reexamine the foundations of linear logic, developing a system of natural deduction following Martin-L ¨ of's separation of judgments from propositions. Our construction yields a clean and elegant formulation that accounts for a rich set of multiplicative, additive, and exponential connectives, extending dual intuitionistic linear logic but differing… (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)

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)

Focusing is traditionally seen as a means of reducing inessential non-determinism in backward-reasoning strategies such as uniform proof-search or tableaux systems. In this paper we construct a form of focused derivations for propositional linear logic that is appropriate for forward reasoning in the inverse method. We show that the focused inverse method… (More)

It is well-known that focusing striates a sequent derivation into phases of like polarity where each phase can be seen as inferring a synthetic connective. We present a sequent calculus of synthetic connectives based on neutral proof patterns , which are a syntactic normal form for such connectives. Different focusing strategies arise from different… (More)