# Higher-Order Illative Combinatory Logic

@article{Czajka2013HigherOrderIC, title={Higher-Order Illative Combinatory Logic}, author={Lukasz Czajka}, journal={The Journal of Symbolic Logic}, year={2013}, volume={78}, pages={837 - 872} }

Abstract We show a model construction for a system of higher-order illative combinatory logic thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order intuitionistic predicate logic with second-order propositional quantifiers into the system of Barendregt, Bunder and Dekkers, which gives a partial answer to a question posed by these authors.

## 6 Citations

### Semantic Consistency Proofs for Systems of Illative Combinatory Logic

- Computer Science
- 2015

The strongest of these systems essentially incorporates full extensional classical higher-order logic extended with dependent function types, dependent sums, subtypes and W-types, which allows to interpret a great deal of mathematics in this system.

### Semantic Consistency Proofs for Systems of Illative Combinatory Logic

- Philosophy
- 2015

Illative systems of combinatory logic or lambda-calculus consist of type-free combinatory logic or lambda-calculus extended with additional constants intended to represent logical notions. In fact,…

### BUNDER’S PARADOX

- PhilosophyThe Review of Symbolic Logic
- 2020

It is shown that a paradox that arises in illative logic is thought to be inconsistent, but this isn’t so, by providing a nonempty class of models that establishes its consistency.

### Partiality and Recursion in Higher-Order Logic

- MathematicsFoSSaCS
- 2013

This paper presents an illative system of classical higher-order logic with subtyping and basic inductive types, and shows conservativity of $\ensuremath{{\cal I}}_s$ over classical first- order logic.

### A Shallow Embedding of Pure Type Systems into First-Order Logic

- Computer ScienceTYPES
- 2016

A shallow embedding of logical proof-irrelevant Pure Type Systems into minimal first-order logic is defined, which forms a basis of the translations used in the recently developed CoqHammer automation tool for dependent type theory.

### Semantyczne dowody niesprzeczności systemów Illatywnej

- 2015

Illatywne systemy logiki kombinatorycznej bądź rachunku lambda rozszerzają beztypowy rachunek kombinatorów bądź rachunek lambda o dodatkowe stałe mające na celu reprezentację pojęć logicznych. W…

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