Related papers: Riesz Logic
A logic family is a bunch of logics that belong together in some way. First-order logic is one of the examples. Logics organized into a structure occurs in abstract model theory, institution theory and in algebraic logic. Logic families…
This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over…
A major target of linguistics and cognitive science has been to understand what class of learning systems can acquire the key structures of natural language. Until recently, the computational requirements of language have been used to argue…
Can neural nets learn logic? We approach this classic question with current methods, and demonstrate that recurrent neural networks can learn to recognize first order logical entailment relations between expressions. We define an artificial…
A new type of deterministic (non-probabilistic) computer logic system inspired by the stochasticity of brain signals is shown. The distinct values are represented by independent stochastic processes: independent voltage (or current) noises.…
Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes.…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
Truncated Riesz spaces was first introduced by Fremlin in the context of real-valued functions. An appropriate axiomatization of the concept was given by Ball. Keeping only the first Ball's Axiom (among three) as a definition of truncated…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
Current large language models reason in isolation. Although it is common to sample multiple reasoning paths in parallel, these trajectories do not interact, and often fail in the same redundant ways. We introduce LACE, a framework that…
A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich's…
Automated reasoning is critical in domains such as law and governance, where verifying claims against facts in documents requires both accuracy and interpretability. Recent work adopts structured reasoning pipelines that translate natural…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
The approach described here allows to use the fuzzy Object Based Representation of imprecise and uncertain knowledge. This representation has a great practical interest due to the possibility to realize reasoning on classification with a…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…
Current breakthroughs in natural language processing have benefited dramatically from neural language models, through which distributional semantics can leverage neural data representations to facilitate downstream applications. Since…
We introduce residuated ortholattices as a generalization of -- and environment for the investigation of -- orthomodular lattices. We establish a number of basic algebraic facts regarding these structures, characterize orthomodular lattices…
New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and…
Categories such as animal or furniture are acquired at an early age and play an important role in processing, organizing, and communicating world knowledge. Categories exist across cultures: they allow to efficiently represent the…