## 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:**