Topics: Formal Systems (Symbolic Systems) , Logic and Foundations of Mathematics, Computation.

Logic is a formalization of reasoning (declaration calculus at the most fundamental level).

Logic is a tool for representing statements, arguments and propositions ; and computing on them for the inference of valid conclusions.

Logic thelos in computing valid conclusions from a set premises.

Logic: is the study of logical frameworks.

Logical Framework: Set of Premises → Conclusion.

Dal lat. logĭca, dal gr. logikḗ (tékhnē) ‘(l'arte) della logica’, der. dell'agg. logikós ‘logico’. Science of Exact Reasoning.

¿What reliable methods do we have for inference and it’s evaluation Proposititons → Conclusions? That’s the job of a logicism.

A "logical representation" refers to a conceptual or abstract depiction of information or entities, emphasizing the relationships, structures, and rules that govern them without necessarily reflecting a direct physical or concrete manifestation.

Extensionality: …

Intensionality: …

Logical representation of reality involves breaking down the components of reality into structured and formalized elements that can be manipulated and reasoned about logically.

Logical Systems are structured frameworks for formal reasoning that use symbols and rules to represent and manipulate propositions, relations, and inferences to derive conclusions and solve problems.

Formal Language: …

Formal System: Formal Language + Deduction Model (Semantics Models).

Well-define formula: …

Automata Theory: Automata theory deals with the definitions and properties of mathematical models of computations.

Complexity Theory: How hard is a problem? What makes a problem hard? Note hard means computational resource intensive.

Computational Theory: Is This Problem Solvable?

Structural rules are general inference rules that apply to all types of premises, regardless of their specific logical content. They govern the structure of proofs rather than the manipulation of specific logical connectives. This is what distinguishes them from logical rules, which define how particular logical operators (e.g., ∧, ∨, →, ¬) behave.