Related papers: A Set-Theoretic Decision Procedure for Quantifier-…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
It is introduced the using of generation lexicographical procedure for multicriteria decision-making problems.
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
We rely on the strength of linguistic and philosophical perspectives in constructing a framework that offers a unified explanation for presuppositions and existential commitment. We use a rich ontology and a set of methodological principles…
Large language models (LLMs) can face factual limitations when responding to time-sensitive queries about recent events that arise after their knowledge thresholds in the training corpus. Existing search-augmented approaches fall into two…
LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A length-bounded inference is of the form $prov(P,G,n)$ which…
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
Writing declarative models has numerous benefits, ranging from automated reasoning and correction of design-level properties be-fore systems are built, to automated testing and debugging of their implementations after they are built. Alloy…
Query Optimization (QO) has become essential for enhancing Large Language Model (LLM) effectiveness, particularly in Retrieval-Augmented Generation (RAG) systems where query quality directly determines retrieval and response performance.…
We address the following decision problem. Given a numeration system $U$ and a $U$-recognizable set $X\subseteq\mathbb{N}$, i.e. the set of its greedy $U$-representations is recognized by a finite automaton, decide whether or not $X$ is…
The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…
Assessing the quality of outputs generated by generative models, such as large language models and vision language models, presents notable challenges. Traditional methods for evaluation typically rely on either human assessments, which are…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
We give efficient deterministic algorithms for converting randomized query algorithms into deterministic ones. We first give an algorithm that takes as input a randomized $q$-query algorithm $R$ with description length $N$ and a parameter…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
This paper introduces the logic $QLET_{F}$, a quantified extension of the logic of evidence and truth $LET_{F}$, together with a corresponding sound and complete first-order non-deterministic valuation semantics. $LET_{F}$ is a…