## What are the limitations of predicate logic?

One key limitation is that it applies only to atomic propositions. There is no way to talk about properties that apply to categories of objects, or about relationships between those properties. That’s what predicate logic is for.

## What is Decidability and Undecidability?

A language is called Decidable or Recursive if there is a Turing machine which accepts and halts on every input string w. Every decidable language is Turing-Acceptable. A decision problem P is decidable if the language L of all yes instances to P is decidable.

**What is first-order logic used for?**

First-order logic is also known as Predicate logic or First-order predicate logic. First-order logic is a powerful language that develops information about the objects in a more easy way and can also express the relationship between those objects.

### What are the limitations of first-order logic for knowledge representation?

a logic is monotonic if every thing that is entailed by a KB is entailed by a superset of the KB: KB╞ a KBb╞ a. exceptions to default conclusions make a logic non-monotonic. previously assumed flies(opus) until told flies(opus)

### What are the limitations of propositional logic to represent the knowledge base?

Limitations of Propositional logic:

- We cannot represent relations like ALL, some, or none with propositional logic. Example: All the girls are intelligent.
- Propositional logic has limited expressive power.
- In propositional logic, we cannot describe statements in terms of their properties or logical relationships.

**What is Undecidability in theory of automata?**

A problem is undecidable if there is no Turing machine which will always halt in finite amount of time to give answer as ‘yes’ or ‘no’. An undecidable problem has no algorithm to determine the answer for a given input.

## What do you mean by Undecidability define decidable and undecidable languages?

if the language L of all yes instances to P is decidable. An undecidable language maybe a partially decidable language or something else but not decidable. If a language is not even partially decidable , then there exists no Turing machine for that language.

## What is first-order logic examples?

Definition A first-order predicate logic sentence G over S is a tautology if F |= G holds for every S-structure F. Examples of tautologies (a) ∀x.P(x) → ∃x.P(x); (b) ∀x.P(x) → P(c); (c) P(c) → ∃x.P(x); (d) ∀x(P(x) ↔ ¬¬P(x)); (e) ∀x(¬(P1(x) ∧ P2(x)) ↔ (¬P1(x) ∨ ¬P2(x))).

**What are the limitations of propositional logic as a tool for knowledge representation?**

We cannot use propositional logic to establish the truth of a proposition that isn’t given as a premise, or which can’t be inferred by the laws of inference. In particular, we cannot use propositional logic to reason about propositions that obey laws (such as arithmetic laws) beyond the logical inference system.

### Is first order logic undecidable?

The Undecidability of First Order Logic A first order logic is given by a set of function symbols and a set of predicate symbols. Each function or predicate symbol comes with an arity, which is natural number. Function symbols of arity 0 are known as constant symbols. Now termsare recursively defined by variables are terms, and

### Are product logics of the form L × Ku undecidable?

The undecidability of the remaining product logics of the form L × Ku —save S52C × Ku —now follows from the reductions of Table 7.1. Finally, S52C × Ku is undecidable, because Ku × Ku is undecidable ( Theorem 5.37) and polynomially reducible to S52C × Ku ( Table 7.1 ).

**What is the completeness theorem for first order logic?**

The completeness theorem for first order logic says that a formula is provable from the laws of first order logic (not given here) if and only if it is true in under all possible interpretations, i.e. regardless of the meaning of the function and predicate symbols.

## Can a theory be undecidable from another?

Only in exceptional cases can a theory for which the decision problem is discussed be obtained from another theory, which is known to be undecidable, simply by omitting finitely many sentences from the axiom system of the latter.