Related papers: Mixed Logic and Storage Operators
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
Linear type systems need to keep track of how programs use their resources. The standard approach is to use context splits specifying how resources are (disjointly) split across subterms. In this approach, context splits redundantly echo…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
The standard oracle operator corresponding to a function f is a unitary operator that computes this function coherently, i.e. it maintains superpositions. This operator acts on a bipartite system, where the subsystems are the input and…
Delimited control operator shift0 exhibits versatile capabilities: it can express layered monadic effects, or equivalently, algebraic effects. Little did we know it can express lambda calculus too! We present $ \Lambda_\$ $, a call-by-value…
We study a classical realizability model (in the sense of J.-L. Krivine) arising from a model of untyped lambda calculus in coherence spaces. We show that this model validates countable choice using bar recursion and bar induction.
Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…
Separation logic is used to reason locally about stateful programs. State of the art program logics for higher-order store are usually built on top of untyped operational semantics, in part because traditional denotational methods have…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…
We present an extension of the second-order logic AF2 with iso-style inductive and coinductive definitions specifically designed to extract programs from proofs a la Krivine-Parigot by means of primitive (co)recursion principles. Our logic…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
Materialisation facilitates Datalog reasoning by precomputing all consequences of the facts and the rules so that queries can be directly answered over the materialised facts. However, storing all materialised facts may be infeasible in…
This paper seeks to apply categorical logic to the design of artificial intelligent agents that reason symbolically about objects more richly structured than sets. Using Johnstone's sequent calculus of terms- and formulae-in-context, we…
J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e. symmetric extensions. We also provide a new…
In the last decade, key-value data storage systems have gained significantly more interest from academia and industry. These systems face numerous challenges concerning storage space- and read optimization. There exists a large potential…
Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and…