diff --git a/content/list-of-definitions/logic-and-ai/index.md b/content/list-of-definitions/logic-and-ai/index.md new file mode 100644 index 00000000..40da9c71 --- /dev/null +++ b/content/list-of-definitions/logic-and-ai/index.md @@ -0,0 +1,39 @@ +--- +title: Logic and AI +subtitle: test +author: Annefleur de Haan +weight: 1 +params: + id: txt-laa +--- + +| Concept | Definition | +|----------------------------------------|------------| +| AI | The study of the models and replication of _intelligent behavior_ in machines or systems, the field focused on creating machines or systems that exhibit behaviors deemed intelligent by human standards.| +| Classical logic | The standard formal system of logic that assumes every proposition is either true or false (principle of bivalence) and that contradictions cannot be true (principle of non-contradiction). It forms the basis of much of modern mathematics and deductive reasoning. | +| Conclusion | A proposition that follows logically from premises within an argument. The conclusion of an inference is what's being inferred or established. It is the statement whose truth is supported or entailed by the given propositions in an argument.| +| Formal derivations | Model of stepwise valid inference based on logical rules. It is a finite sequence of formulas in a formal system where each formula is either an axiom or follows from earlier formulas by rules of inference. It demonstrates, step by step, how a conclusion can be logically deduced from a set of premises using only syntactic rules, independent of any interpretation or meaning. | +| Formal language | A set of strings constructed from a finite alphabet according to specific syntactic rules (grammar). It is abstract and independent of meaning, designed to capture the form of expressions rather than their content. | +| Formal models | Structure that interprets the symbols and formulas of a formal language in a way that allows one to evaluate their truth or falsity. | +| (First) incompleteness theorem | Gödel’s result showing that any sufficiently expressive, consistent formal system cannot prove all true statements expressible within its own language. Every logical system that is free of internal contradictions and models basic mathematical reasoning, has a mathematical statement in it that is undecidable in the system.| +| If-then rules | Symbolic representations of conditional statements used in rule-based systems: if condition A, then consequence B. The words _if_ and _then_ connect the antecedent to the consequent.| +| Indicators | Logical cues that signal the role of statements, i.e., the premises or the inference. | +| Inference | The process of deriving new propositions (conclusions) from a set of given propositions (premises) according to rules of logic. It formalizes how knowledge propagates under constraints of logical validity. Types of inference: deductive inference and inductive inference. | +| Intuitionistic Logic | Assumes that truth needs to be constructed. A form of logic rejecting the law of the excluded middle, emphasizing constructivist proof over truth-as-correspondence. | +| Logical formulas | A well-formed expression constructed from symbols of a formal language of logic that represents a proposition or a relationship between propositions. Logical formulas are the primary vehicles for expressing statements, arguments, and proofs in formal logic. | +| Logical laws | Universally valid principles or tautologies within a given logical system. They describe invariant relationships between logical formulas and form the basis of formal reasoning. In classical logic, these laws hold independently of the content of the formulas—they are purely a function of logical form. | +| Logic | The formal study of valid reasoning. It investigates the principles that distinguish correct from incorrect inferences, abstracting away from specific content to focus on structure. In both mathematics and philosophy, logic provides the foundational framework for evaluating arguments, constructing proofs, and modeling rational thought. | +| Machine learning | Subfield of artificial intelligence (AI) focused on developing algorithms that allow computers to learn patterns from data and make predictions or decisions without being explicitly programmed for each specific task. | +| Metalogic | The study of the properties of formal logical systems themselves, rather than the content of those systems. While logic investigates what follows from what within a system (e.g., deriving conclusions from premises), metalogic steps outside the system to examine its structure, capabilities, and limitations.| +| Premise | A statement assumed to be true within an argument from which a conclusion is derived. The conclusion is based on the premises of the inferences.| +| Proof theory | A model of stepwise valid inference. The study of formal proofs as mathematical objects, often used to analyze the structure and derivability in logical systems. | +| Semantics | A model of the meaning of the premises and conclusions. The branch of logic dealing with meaning and truth in formal languages, often via interpretations or models.| +| Subsymbolic AI | AI approach that operate on distributed representations rather than explicit symbols. Subsymbolic AI prefers conditional probabilities and inductive inference over if-then rules and deductive inference.| +| Symbolic AI | An approach to AI in which knowledge and reasoning are represented using explicit symbols and formal rules. It models intelligence as a process of manipulating symbolic representations of concepts, objects, and relationships—often through logical inference. | +| Syntax | The branch of logic that studies the formal structure of expressions in a logical language, without reference to their meaning. It specifies the rules that determine which combinations of symbols count as well-formed formulas in a given formal system. It includes an alphabet, formation rules, terms and objects. | +| System 1 thinking | Refers to the fast, automatic, intuitive, and effortless mode of cognition described in dual-process theories of the mind, particularly as articulated by Daniel Kahneman in Thinking, Fast and Slow. It contrasts with System 2, which is slower, deliberative, and analytic.| +| System 2 thinking | Refers to the slow, deliberate, effortful, and conscious mode of cognitive processing, as characterized in dual-process theories of reasoning—most notably in Daniel Kahneman’s Thinking, Fast and Slow. It operates in contrast to the fast, automatic, and intuitive System 1.| +| Undecidability theorem | A theorem which establishes that there exist well-defined decision problems in formal logic and computation that cannot be solved by any algorithm. That is, there is no mechanical procedure that can always give a yes-or-no answer to every instance of the problem. | +| Validity | A central semantic notion in logic. A formula or argument is valid if, under every interpretation (or in every model), the truth of its premises guarantees the truth of its conclusion. Validity is thus about truth preservation across all possible situations consistent with the formal semantics of the system.| + + diff --git a/content/list-of-definitions/logic-and-ai/info.md b/content/list-of-definitions/logic-and-ai/info.md new file mode 100644 index 00000000..50b1c113 --- /dev/null +++ b/content/list-of-definitions/logic-and-ai/info.md @@ -0,0 +1 @@ +Here you can find a list of important definitions. Note: these definitions are not sufficient to understand the concept in full, you should read the textbook, practice and attent the lectures and tutorials to gain real understanding. This list is meant to refresh some basics.