相关论文: The taming of recurrences in computability logic t…

A proof procedure, in the spirit of the sequent calculus, is proposed to check the validity of entailments between Separation Logic formulas combining inductively defined predicates denoted structures of bounded tree width and theory…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…

We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are…

"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…

We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…

One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…

We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…

Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…

The preferential conditional logic PCL, introduced by Burgess, and its extensions are studied. First, a natural semantics based on neighbourhood models, which generalise Lewis' sphere models for counterfactual logics, is proposed. Soundness…

The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…

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…

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…

This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…

Circular proofs, introduced by Daniyar Shamkanov, are proofs in which assumptions are allowed that are not axioms but do appear at least twice along a branch. Shamkanov has shown that a formula belongs to the provability logic GL exactly if…

The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…

We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…

This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…