Related papers: Interleaving Logic and Counting
Based on ideas of quantum theory of open systems and psychological dual system theory we propose two novel versions of Non-Boolean logic. The first version can be interpreted in our opinion as simplified description of primitive…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a…
Commonsense reasoning has long been considered as one of the holy grails of artificial intelligence. Most of the recent progress in the field has been achieved by novel machine learning algorithms for natural language processing. However,…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
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…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
Language models struggle with handling numerical data and performing arithmetic operations. We hypothesize that this limitation can be partially attributed to non-intuitive textual numbers representation. When a digit is read or generated…
Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted…
We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi$ (in $\mathcal{L}_{\omega,\omega}$) is…
The difference between object-language and metalanguage is crucial for logical analysis, but has yet not been examined for the field of computer science. In this paper the difference is examined with regard to inferential relations. It is…
Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic…
There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based. Usually, interval-based temporal reasoning deals with points as a particular case of duration-less intervals. A recent…