DeepAI

# Axiomatizations and Computability of Weighted Monadic Second-Order Logic

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 formulas output are evaluated. Gastin and Monmege (2018) gave abstract semantics for a version of weighted monadic second-order logic to give a more general and modular proof of the equivalence of the logic with weighted automata. We focus on the abstract semantics of the logic and we give a complete axiomatization both for the full logic and for a fragment without general sum, thus giving a more fine-grained understanding of the logic. We discuss how common decision problems for logical languages can be adapted to the weighted setting, and show that many of these are decidable, though they inherit bad complexity from the underlying first- and second-order logics. However, we show that a weighted adaptation of satisfiability is undecidable for the logic when one uses the abstract interpretation.

• 6 publications
• 2 publications
01/25/2023

### Lecture Notes on Monadic First- and Second-Order Logic on Strings

These notes present the essentials of first- and second-order monadic lo...
02/21/2019

### Aperiodic Weighted Automata and Weighted First-Order Logic

By fundamental results of Schützenberger, McNaughton and Papert from the...
01/18/2019

### First-Order vs. Second-Order Encodings for LTLf-to-Automata Translation

Translating formulas of Linear Temporal Logic (LTL) over finite traces, ...
12/04/2017

### A Second-Order Approach to Complex Event Recognition

Complex Event Recognition (CER for short) refers to the activity of dete...
02/15/2019

### Coalgebra Learning via Duality

Automata learning is a popular technique for inferring minimal automata ...
12/26/2017

### On the Semantics of Intensionality and Intensional Recursion

Intensionality is a phenomenon that occurs in logic and computation. In ...
02/15/2022

### The pseudofinite monadic second order theory of words

We analyse the pseudofinite monadic second order theory of words over a ...