Related papers: Abstract computation over first-order structures. …
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
A model of computation is abstract if, when applied to any algebra, the resulting programs for computable functions and sets on that algebra are invariant under isomorphisms, and hence do not depend on a representation for the algebra.…
Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…
Whether explicit or implicit, sets are a critical part of many pieces of software. As a result, it is necessary to develop abstractions of sets for the purposes of abstract interpretation, model checking, and deductive verification.…
Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…
We consider sets/relations/computations defined by *Elementary Inference Systems* I, which are obtained from Smullyan's *elementary formal systems* using Gentzen's notation for inference rules, and proof trees for atoms P(t_1,...,t_n),…
The need for modelling causal knowledge at different levels of granularity arises in several settings. Causal Abstraction provides a framework for formalizing this problem by relating two Structural Causal Models at different levels of…
The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
Starting from Gurevich's thesis for sequential algorithms (the so-called "sequential ASM thesis"), we propose a characterization of the behaviour of sequential algorithms enriched with reflection. That is, we present a set of postulates…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…