## Logical Reasoning Problem and Solutions
### Overview
The image presents a logical reasoning problem and two different approaches to solving it: Logic-LM and SymPro-LM. The problem is stated at the top, followed by the Logic-LM approach on the left and the SymPro-LM approach on the right.
### Components/Axes
* **Problem Statement:** A series of statements defining relationships between different entities (Jompuses, Wumpuses, Dumpuses, etc.) and their properties (dull, opaque, floral, etc.). The final question is "Is Sam Dull?".
* **Logic-LM (Left Side):**
* **Predicates:** Defines the meaning of terms like "Wumpus(x, bool)" as "Does x belong to Wumpus?".
* **Facts:** States "Dumpus(Sam, True)", meaning Sam is a Dumpus.
* **Rules:** Defines logical implications, such as "Wumpus(x, True) >>> Opaque(x, True)", meaning if something is a Wumpus, it is opaque.
* **SymPro-LM (Right Side):**
* **Properties Dictionary:** Defines the properties of each entity using a Python dictionary. For example, "jompus": {"dull": False} means a Jompus is not dull.
* **Rule Implementation:** Python code that adds rules based on the properties dictionary using loops and conditional statements. It uses a solver `s` and adds implications using `s.add(Implies(...))`.
### Detailed Analysis or ### Content Details
**Problem Statement:**
* Jompuses are not dull.
* Every wumpus is opaque.
* Wumpuses are dumpuses.
* Every dumpus is not floral.
* Dumpuses are numpuses.
* Each numpus is not luminous.
* Each numpus is a vumpus.
* Every vumpus is large.
* Vumpuses are tumpuses.
* Every tumpus is not orange.
* Every tumpus is a zumpus.
* Zumpuses are dull.
* Every zumpus is an impus.
* Every impus is spicy.
* Every impus is a rompus.
* Rompuses are not temperate.
* Every rompus is a yumpus.
* Sam is a dumpus.
* Is Sam Dull?
**Logic-LM:**
* **Predicates:**
* Wumpus($x, bool) ::: Does x belong to Wumpus?
* Opaque($x, bool) ::: Is x opaque?
* Numpus($x, bool) ::: Does x belong to Numpus?
* Vumpus($x, bool) ::: Does x belong to Vumpus?
* Large($x, bool) ::: Is x large?
* Tumpus($x, bool) ::: Does x belong to Tumpus?
* **Facts:**
* Dumpus(Sam, True)
* **Rules:**
* Wumpus($x, True) >>> Opaque($x, True)
* Wumpuses($x, True) >>> Dumpus($x, True)
* Vumpus($x, True) >>> Large($x, True)
* Vumpuses($x, True) >>> Tumpus($x, True)
**SymPro-LM:**
* **Properties Dictionary:**