Related papers: Interleaving Logic and Counting
Datalog is one of the best-known rule-based languages, and extensions of it are used in a wide context of applications. An important Datalog extension is Disjunctive Datalog, which significantly increases the expressivity of the basic…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…
We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
This paper establishes model-theoretic properties of $\mathrm{FOE}^{\infty}$, a variation of monadic first-order logic that features the generalised quantifier $\exists^\infty$ (`there are infinitely many'). We provide syntactically defined…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
We explore end-to-end trained differentiable models that integrate natural logic with neural networks, aiming to keep the backbone of natural language reasoning based on the natural logic formalism while introducing subsymbolic vector…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus…
The relationship between Lexical-Functional Grammar (LFG) functional structures (f-structures) for sentences and their semantic interpretations can be expressed directly in a fragment of linear logic in a way that explains correctly the…
Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as proving mathematical theorems and building mathematical theories, common sense reasoning, learning, language…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…