Related papers: Non-distributive description logic
We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…
This paper presents LEXR, a framework for explaining the decision making of recurrent neural networks (RNNs) using a formal description language called Linear Temporal Logic (LTL). LTL is the de facto standard for the specification of…
We give an optimal (EXPTIME), sound and complete tableau-based algorithm for deciding satisfiability for propositional dynamic logic with converse (CPDL) which does not require the use of analytic cut. Our main contribution is a sound…
We introduce the notion of contrastive ABox explanations to answer questions of the type "Why is a an instance of C, but b is not?". While there are various approaches for explaining positive entailments (why is C(a) entailed by the…
This paper describes a technique for inferring temporal-logic properties for sets of finite data streams. Such data streams arise in many domains, including server logs, program testing, and financial and marketing data; temporal-logic…
The theory of bounded, distributive lattices provides the appropriate language for describing directionality and asymptotics in dynamical systems. For bounded, distributive lattices the general notion of `set-difference' taking values in a…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
Abstract algebraic logic is a theory that provides general tools for the algebraic study of arbitrary propositional logics. According to this theory, every logic L is associated with a matrix semantics Mod*(L). This paper is a contribution…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
We consider the problem of fast time-series data clustering. Building on previous work modeling the correlation-based Hamiltonian of spin variables we present an updated fast non-expensive Agglomerative Likelihood Clustering algorithm…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Formal programming language semantics are imperative when trying to verify properties of programs in an automated manner. Using a new approach, Din et al. strengthen the ability of reasoning about concurrent programs by proposing a modular…
A finitary propositional logic can be given an algebraic reading in two different ways: by translating formulas into equations and logical rules into quasi-equations, or by translating logical rules directly into equations. The former type…
In this paper we describe a mechanism to improve Information Retrieval (IR) on the web. The method is based on Formal Concepts Analysis (FCA) that it is makes semantical relations during the queries, and allows a reorganizing, in the shape…
We prove The Equivalence Theorem: structurally complete knowledge representation requires exactly four mutually entailing capabilities -- n-ary relationships with attributes, temporal validity, uncertainty quantification, and causal…
We present a lattice of distributed program specifications, whose ordering represents implementability/refinement. Specifications are modelled by families of subsets of relative execution traces, which encode the local orderings of state…
We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…