# First-Order Stable Model Semantics with Intensional Functions

arXiv: https://arxiv.org/abs/2307.10225 · HTML: https://mlsanity.com/paper/2307.10225/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 66 references that are in the map.
- First posted on arXiv 15 Jul 2023.

## Builds on (most cited first, 4 of 4)

- [Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories](https://mlsanity.com/paper/1606.07860/) (2016)
- [Satisfiability Modulo ODEs](https://mlsanity.com/paper/1310.8278/) (2013)
- [A Functional View of Strong Negation in Answer Set Programming](https://mlsanity.com/paper/1312.6130/) (2013)
- [Representing Hybrid Automata by Action Language Modulo Theories](https://mlsanity.com/paper/1707.06387/) (2017)

## Built on by (most cited first, 3 of 3)

- [Unit Testing in ASP Revisited: Language and Test-Driven Development Environment](https://mlsanity.com/paper/2401.02153/) (2024)
- [Recursive Aggregates as Intensional Functions in Answer Set Programming: Semantics and Strong Equivalence](https://mlsanity.com/paper/2412.10975/) (2024)
- [Relating Answer Set Programming and Many-sorted Logics for Formal Verification](https://mlsanity.com/paper/2502.09230/) (2025)

## Abstract (arXiv)

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee, and Lifschitz to allow intensional functions -- functions that are specified by a logic program just like predicates are specified. We show that many known properties of the stable model semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of ASP. Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non-intensional ones.