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We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
It is well-known that freeness and linearity information positively interact with aliasing information, allowing both the precision and the efficiency of the sharing analysis of logic programs to be improved. In this paper we present a…
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
Abstraction is a key verification technique to improve scalability. However, its use for neural networks is so far extremely limited. Previous approaches for abstracting classification networks replace several neurons with one of them that…
The core challenge in designing an effective static program analysis is to find a good program abstraction -- one that retains only details relevant to a given query. In this paper, we present a new approach for automatically finding such…
Conceiving of premises as collected into sets or multisets, instead of sequences, may lead to triviality for classical and intuitionistic logic in general proof theory, where we investigate identity of deductions. Any two deductions with…
Thanks to the locality principle, separation logics support modular, scalable analysis of large codebases by relying on local axioms and frame rules to focus only on the heap fragments required for verification. However, depending on the…
An abstraction can be used to relate two structural causal models representing the same system at different levels of resolution. Learning abstractions which guarantee consistency with respect to interventional distributions would allow one…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
This paper studies relative unification and admissibility in the intuitionistic logic. We generalize results of [Ghilardi, 1999; Iemhoff, 2001a] and prove them relative in NNIL(par) propositions, the class of propositions with No Nested…
This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract, syntax-free contraction-weakening proofs; (3) distribution; (4)…
For years, independence has been considered as an important concept in many disciplines. Nevertheless, we present the first research that investigates the discovery problem of independence in data. In its arguably simplest form,…
G\"odel's Dialectica interpretation was designed to obtain a relative consistency proof for Heyting arithmetic, to be used in conjunction with the double negation interpretation to obtain the consistency of Peano arithmetic. In recent…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The growing need for trustworthy machine learning has led to the blossom of interpretability research. Numerous explanation methods have been developed to serve this purpose. However, these methods are deficiently and inappropriately…
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…