Why are these formulas not well-formed in syllogistic logic?


Which of the following is not a well-formed formula WFF )?

1 Expert Answer

((∼A)∨(∼B)) is not a well formed formula. At most, there can only be a pair of parentheses per binary (or dyadic) connective in a well formed formula. Since there is only one binary/dyadic connective in ‘v’, there should be only be one pair of parentheses, rather than three pairs.

What makes a well-formed formula?

Well-Formed Formula(WFF) is an expression consisting of variables(capital letters), parentheses, and connective symbols. An expression is basically a combination of operands & operators and here operands and operators are the connective symbols.

What is well-formed formula in propositional logic?

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language. A formal language can be identified with the set of formulas in the language.

How do you tell if something is a well-formed formula?

It has only three rules:

  1. Any capital letter by itself is a WFF.
  2. Any WFF can be prefixed with “~”. (The result will be a WFF too.)
  3. Any two WFFs can be put together with “•”, “∨”, “⊃”, or “≡” between them, enclosing the result in parentheses. (This will be a WFF too.)
See also  Need help in knowing what fallacy my statement undergoes

What is well-formed formula in discrete mathematics?

Well Formed Formula (wff) is a predicate holding any of the following − All propositional constants and propositional variables are wffs. If x is a variable and Y is a wff, ∀xY and ∃xY are also wff. Truth value and false values are wffs. Each atomic formula is a wff.

What is a closed formula in logic?

closed formula (plural closed formulas or closed formulae) (logic) A formula which has no free occurrences of variables; or equivalently, in which all occurrences of variables are bound.

What is the difference between propositional logic and predicate logic?

Propositional logic is the logic that deals with a collection of declarative statements which have a truth value, true or false. Predicate logic is an expression consisting of variables with a specified domain. It consists of objects, relations and functions between the objects.

What are the limitations of propositional logic?

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 are the limitations of proposition logic How can we overcome that using predicate logic?

We can use propositional logic to validate the form of an argument that takes us from premises to a conclusion. 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.

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.

See also  Authors that compare nationalism to religion

What is one advantage or disadvantage of FOL?

It is also called first order logic (FOL). The obvious advantage is that we can say a lot more. One disadvantage is that while theorem proving is still sound, (that is, we can always prove true theorems), it is now undecidable (the theorem prover may never halt on untrue statements).

What are the advantages of predicate logic?

An additional benefit of predicate logic (other than the purely logical benefit concerning the study of logical validity) is the elimination of ambiguities once a natural language sentence is translated into its symbolic language.