Related papers: Superposition as a logical glue
Mathematical reasoning is one of the crucial abilities of general artificial intelligence, which requires machines to master mathematical logic and knowledge from solving problems. However, existing approaches are not transparent (thus not…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
We present a system capable of automatically solving combinatorial logic puzzles given in (simplified) English. It involves translating the English descriptions of the puzzles into answer set programming(ASP) and using ASP solvers to…
Answering complex questions is a challenging task that requires question decomposition and multistep reasoning for arriving at the solution. While existing supervised and unsupervised approaches are specialized to a certain task and involve…
Automaton models are often seen as interpretable models. Interpretability itself is not well defined: it remains unclear what interpretability means without first explicitly specifying objectives or desired attributes. In this paper, we…
In this paper, we delve into the study of epistemic logics, interpreted through similarity models based on weighted graphs. We explore eight languages that extend the traditional epistemic language by incorporating modalities of common,…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…
With the ever-growing amounts of textual data from a large variety of languages, domains, and genres, it has become standard to evaluate NLP algorithms on multiple datasets in order to ensure consistent performance across heterogeneous…
This paper investigates an unsupervised approach towards deriving a universal, cross-lingual word embedding space, where words with similar semantics from different languages are close to one another. Previous adversarial approaches have…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
In this paper we describe an algorithm for implicitizing rational hypersurfaces in case there exists at most a finite number of base points. It is based on a technique exposed in math.AG/0210096, where implicit equations are obtained as…
Language models are often evaluated with scalar metrics like accuracy, but such measures fail to capture how models internally represent ambiguity, especially when human annotators disagree. We propose a topological perspective to analyze…
Rewriting logic is naturally concurrent: several subterms of the state term can be rewritten simultaneously. But state terms are global, which makes compositionality difficult to achieve. Compositionality here means being able to decompose…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end,…
In this paper we show that subsumption problems in lightweight description logics (such as $\mathcal{EL}$ and $\mathcal{EL}^+$) can be expressed as uniform word problems in classes of semilattices with monotone operators. We use…
The ability to manipulate logical-mathematical symbols (LMS), encompassing tasks such as calculation, reasoning, and programming, is a cognitive skill arguably unique to humans. Considering the relatively recent emergence of this ability in…
Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…