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all, none, some, or not all of something is what your going to deal with mostly.
the hardest thing for me is translation into PD (predicate logic).
upside down capital A "∀" means for everything in the universe of discourse you are tramslating.
example : all Greeks are human
(∀x) (Gx > Hx) "for all x, if x is greek, then x is human"
this basically means the universe of discourse is Greeks (for all G basically).
now this ∀ symbol is called a quantifier. it is a universal quantifier... hence for "ALL" x
now there is another quantifier. an existential quantifier. this is different from universal
because it is not for every x, it is for AT LEAST ONE (which means there is an x) or not all x.
this symbol is a backwards E "∃"
example: there is a greek that is human
(∃x) (Gx & Hx) "there exists an x, (such that, or and) x is greek and x is human"
notice that the universal is a "if, then" or (>) statement and the existential is a "&" statement. for the most part this is how they work but there are some instances were both can be implemented...
example: all greek athelete's are human
(∀x) (Gx & Ax) > Hx "for all x, if x is a greek and an athelete,
then x is a human"
this is mostly predicate stuff but hopefully a good start to the harder stuff young blood.
What else can I help you with?
What is the difference between predicate and propositional logic?
in propositional logic a complete sentence can be presented as an atomic proposition. and complex sentences can be created using AND, OR, and other operators.....these propositions has only true of false values and we can use truth tables to define them... like book is on the table....this is a single proposition... in predicate logic there are objects, properties, functions (relations) are involved.
What are the 3 division of logic?
The three main divisions of logic are formal logic, informal logic, and symbolic logic. Formal logic focuses on the structure and form of arguments, using systems like propositional and predicate logic. Informal logic deals with everyday reasoning and argumentation, emphasizing the content and context of arguments. Symbolic logic uses mathematical symbols to represent logical expressions, allowing for precise manipulation and analysis of logical statements.
What is predicate calculus?
Predicate calculus is the axiomatic form of predicate logic.
In the Boolean interpretation of propositional logic?
Have a look at this website.. It answers your question very nicely. http://www.rbjones.com/rbjpub/logic/log003.htm
What Is a statement that is either true or false?
A statement that is either true or false is known as a propositional statement or a proposition. For example, "The sky is blue" is a propositional statement because it can be evaluated as true or false based on the conditions at a given time. Propositional logic relies on these types of statements to form logical arguments and reasoning.
1 What are the differences between propositional and first order logic?
Difference between Propositonal and Predicate logic
What are the examples of formal logic?
Examples of formal logic include propositional logic, predicate logic, modal logic, and temporal logic. These systems use symbols and rules to represent and manipulate logical relationships between statements. Formal logic is used in mathematics, computer science, philosophy, and other fields to reason rigorously and draw valid conclusions.
What is the difference between predicate and propositional logic?
in propositional logic a complete sentence can be presented as an atomic proposition. and complex sentences can be created using AND, OR, and other operators.....these propositions has only true of false values and we can use truth tables to define them... like book is on the table....this is a single proposition... in predicate logic there are objects, properties, functions (relations) are involved.
What is subject in proposition logic?
In propositional logic, a subject refers to the entities or objects that are being described or discussed in a particular proposition. It is typically the noun or noun phrase that the predicate is providing information about.
How predicate calculus is differ from propositional calculus?
The predicate calculus extends the propositional calculus by adding quantifiers such as 'all' (written with an upside-down 'A') and 'some' (written with a backwards 'E').
How can we ensure the soundness and completeness of propositional logic?
To ensure the soundness and completeness of propositional logic, we must verify that all logical arguments are valid and that all valid conclusions can be reached using the rules of propositional logic. Soundness means that the premises of an argument logically lead to the conclusion, while completeness means that all valid conclusions can be derived from the premises. This can be achieved through rigorous proof methods and adherence to the rules of propositional logic.
What are the 3 division of logic?
The three main divisions of logic are formal logic, informal logic, and symbolic logic. Formal logic focuses on the structure and form of arguments, using systems like propositional and predicate logic. Informal logic deals with everyday reasoning and argumentation, emphasizing the content and context of arguments. Symbolic logic uses mathematical symbols to represent logical expressions, allowing for precise manipulation and analysis of logical statements.
How do you study logic?
To study logic, one can start by familiarizing oneself with basic logical principles and concepts such as deductive reasoning, truth tables, and logical fallacies. It is also helpful to practice solving logic puzzles and arguments to improve critical thinking skills. Additionally, studying formal logic systems like propositional and predicate logic can deepen understanding of logical structures and reasoning.
What is predicate calculus?
Predicate calculus is the axiomatic form of predicate logic.
What is the difference between categorical logic and propositional logic?
Categorical logic deals with the relationships between categories or classes of objects, focusing on the inclusion and exclusion of these categories (e.g., all, some, none). It uses terms like "All A are B" to establish connections between different categories. In contrast, propositional logic focuses on the truth values of entire statements or propositions, using logical connectives like "and," "or," and "not" to form complex expressions. Thus, while categorical logic emphasizes relationships between groups, propositional logic centers on the truth conditions of statements.
How can I generate a predicate logic proof using the Predicate Logic Proof Generator?
To generate a predicate logic proof using the Predicate Logic Proof Generator, you need to input the premises and the conclusion of the argument in the appropriate format. The tool will then guide you through the steps to construct a valid proof by applying rules of inference and logical equivalences.
What is propositional logic?
Proposition in logic refers to the statements that are either true or false, but not both. Such kind of statements or sentences are usually called propositions.
