Related papers: Nested Sequents for Intuitionistic Grammar Logics …
We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity.…
In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…
Neural sequence models have achieved great success in sentence-level sentiment classification. However, some models are exceptionally complex or based on expensive features. Some other models recognize the value of existed linguistic…
Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…
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…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
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…
This paper describes a method for compiling a constraint-based grammar into a potentially more efficient form for processing. This method takes dependent disjunctions within a constraint formula and factors them into non-interacting groups…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…