The logical basis for computer programming. Volume 1: Deductive reasoning

Grounded Models as a Basis for Intuitive and Deductive Reasoning: the Acquisition of Logical Categories

Grounded models differ from axiomatic theories in establishing explicit connections between language and reality that are learned through language games. This paper describes how grounded models are constructed by visually grounded autonomous agents playing different types of language games, and explains how they can be used for intuitive reasoning. It proposes a particular language game that c...

Linear Logical Reasoning on Programming

In our paper we follow the development of our approach of regarding programming as logical reasoning in intuitionistic linear logic. We present basic notions of linear logic and its deduction system and we define categorical semantics of linear logic as a symmetric monoidal closed category. Then we construct linear type theory over linear Church’s types involving linear calculus with equational...

Logical basis for the automation of reasoning: Case studies

Logical Basis for the Automation of Reasoning: Case Studies1

Beluga: A Framework for Programming and Reasoning with Deductive Systems

Beluga is an environment for programming and reasoning about formal systems given by axioms and inference rules. It implements the logical framework LF for specifying and prototyping formal systems via higher-order abstract syntax. It also supports reasoning: the user implements inductive proofs about formal systems as dependently typed recursive functions. A distinctive feature of Beluga is th...