Related papers: A new graphical calculus of proofs
Drossopoulou and Noble argue persuasively for the need for a means to express policy in object-capability-based systems. We investigate a practical means to realize their aim via the Curry-Howard isomorphism. Specifically, we investigate…
In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and…
A major reason behind the success of probability calculus is that it possesses a number of valuable tools, which are based on the notion of probabilistic independence. In this paper, I identify a notion of logical independence that makes…
Computability logic is a formal theory of (interactive) computability in the same sense as classical logic is a formal theory of truth. This approach was initiated very recently in "Introduction to computability logic" (Annals of Pure and…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
We propose a new directed graphical representation of utility functions, called UCP-networks, that combines aspects of two existing graphical models: generalized additive models and CP-networks. The network decomposes a utility function…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
A representation theorem relates different mathematical structures by providing an isomorphism between them: that is, a one-to-one correspondence preserving their original properties. Establishing that the two structures substantially…
As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…
We propose a "modal linear logic" to reformulate intuitionistic modal logic S4 (IS4) in terms of linear logic, establishing an S4-version of Girard translation from IS4 to it. While the Girard translation from intuitionistic logic to linear…
Inductive proofs can be represented as proof schemata, i.e. as parameterized sequences of proofs defined in a primitive recursive way. Applications of proof schemata can be found in the area of automated proof analysis where the schemata…
We introduce a new diagrammatic notation for representing the result of (algebraic) effectful computations. Our notation explicitly separates the effects produced during a computation from the possible values returned, this way simplifying…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
Functional languages with strong static type systems have beneficial properties to help ensure program correctness and reliability. Surprisingly, their practical significance in applications is low relative to other languages lacking in…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of…
We found in Homotopy Type Theory (HoTT), a way of representing a first order version of intuitionistic logic (ICL), for intuitionistic calculational logic) where, instead of deduction trees, corresponding linear calculational formats are…
In this paper we introduce a term calculus ${\cal B}$ which adds to the affine $\lambda$-calculus with pairing a new construct allowing for a restricted form of contraction. We obtain a Curry-Howard correspondence between ${\cal B}$ and the…