Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses:
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
Without loss of generality is a frequently used expression in mathematics. The term is used to indicate the assumption that what follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are sufficiently similar to the one presented that proving them follows by essentially the same logic. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases.
Circular reasoning is a logical fallacy in which the reasoner begins with what they are trying to end with. Circular reasoning is not a formal logical fallacy, but a pragmatic defect in an argument whereby the premises are just as much in need of proof or evidence as the conclusion, and as a consequence the argument fails to persuade. Other ways to express this are that there is no reason to accept the premises unless one already believes the conclusion, or that the premises provide no independent ground or evidence for the conclusion. Circular reasoning is closely related to begging the question, and in modern usage the two generally refer to the same thing.
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle. Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction.
A non-monotonic logic is a formal logic whose conclusion relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence. Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to the hypotheses never produces a pruning of its set of conclusions. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. Monotonic logics cannot handle various reasoning tasks such as reasoning by default, abductive reasoning, some important approaches to reasoning about knowledge, and similarly, belief revision.
Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents.
Negation as failure is a non-monotonic inference rule in logic programming, used to derive from failure to derive . Note that can be different from the statement of the logical negation of , depending on the completeness of the inference algorithm and thus also on the formal logic system.
The closed-world assumption (CWA), in a formal system of logic used for knowledge representation, is the presumption that a statement that is true is also known to be true. Therefore, conversely, what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed-world assumption is the open-world assumption (OWA), stating that lack of knowledge does not imply falsity. Decisions on CWA vs. OWA determine the understanding of the actual semantics of a conceptual expression with the same notations of concepts. A successful formalization of natural language semantics usually cannot avoid an explicit revelation of whether the implicit logical backgrounds are based on CWA or OWA.
The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge. While propositional logic can only express facts, autoepistemic logic can express knowledge and lack of knowledge about facts.
The Yale shooting problem is a conundrum or scenario in formal situational logic on which early logical solutions to the frame problem fail. The name of this problem comes from a scenario proposed by its inventors, Steve Hanks and Drew McDermott, working at Yale University when they proposed it. In this scenario, Fred is initially alive and a gun is initially unloaded. Loading the gun, waiting for a moment, and then shooting the gun at Fred is expected to kill Fred. However, if inertia is formalized in logic by minimizing the changes in this situation, then it cannot be uniquely proved that Fred is dead after loading, waiting, and shooting. In one solution, Fred indeed dies; in another solution, the gun becomes mysteriously unloaded and Fred survives.
The concept of a stable model, or answer set, is used to define a declarative semantics for logic programs with negation as failure. This is one of several standard approaches to the meaning of negation in logic programming, along with program completion and the well-founded semantics. The stable model semantics is the basis of answer set programming.
Abductive logic programming (ALP) is a high-level knowledge-representation framework that can be used to solve problems declaratively, based on abductive reasoning. It extends normal logic programming by allowing some predicates to be incompletely defined, declared as abducible predicates. Problem solving is effected by deriving hypotheses on these abducible predicates as solutions of problems to be solved. These problems can be either observations that need to be explained or goals to be achieved. It can be used to solve problems in diagnosis, planning, natural language and machine learning. It has also been used to interpret negation as failure as a form of abductive reasoning.
An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.
The psychology of reasoning is the study of how people reason, often broadly defined as the process of drawing conclusions to inform how people solve problems and make decisions. It overlaps with psychology, philosophy, linguistics, cognitive science, artificial intelligence, logic, and probability theory.
The burden of proof is the obligation on a party in a dispute to provide sufficient warrant for its position.
In information technology a reasoning system is a software system that generates conclusions from available knowledge using logical techniques such as deduction and induction. Reasoning systems play an important role in the implementation of artificial intelligence and knowledge-based systems.
In artificial intelligence and related fields, an argumentation framework is a way to deal with contentious information and draw conclusions from it using formalized arguments.
Victor Witold Marek, formerly Wiktor Witold Marek known as Witek Marek is a Polish mathematician and computer scientist working in the fields of theoretical computer science and mathematical logic.
