Related papers: On Loop Formulas with Variables
Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
We introduce the first order logic of proofs $FOLP^\Box$ in the joint language combining justification terms and binding modalities. The main issue is Kripke--style semantics for this logic. We describe models for $FOLP^\Box$ in terms of…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
Modern data science applications demand solving large-scale optimization problems. The prevalent approaches are first-order methods, valued for their scalability. These methods are implemented to tackle highly irregular problems where…
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…
Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…
Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the…
Dynamical systems theory provides a framework for analyzing iterative processes and evolution over time. Within such systems, repetitive transformations can lead to stable configurations, known as attractors, including fixed points and…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
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…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…
An equational logic program is a set of directed equations or rules, which are used to compute in the obvious way (by replacing equals with ``simpler'' equals). We present static analysis techniques for efficient equational logic…