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Fluent Calculus
The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; the main difference is that situations are considered representations of states. A binary function symbol \circ is used to concatenate the terms that represent facts that hold in a situation. For example, that the box is on the table in the situation s is represented by the formula \exists t . s = on(box,table) \circ t. The frame problem is solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as: : State(Do(move(box,table,floor), s)) \circ on(box,table) = State(s) \circ on(box,floor) This formula states that the state after the move is added the term on(box,floor) and removed the term on(box,table). Axioms specifying that \circ is commutative and non-idempotent are necessary ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Situation Calculus
The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. The main version of the situational calculus that is presented in this article is based on that introduced by Ray Reiter in 1991. It is followed by sections about McCarthy's 1986 version and a logic programming formulation. Overview The situation calculus represents changing scenarios as a set of first-order logic formulae. The basic elements of the calculus are: *The actions that can be performed in the world *The fluents that describe the state of the world *The situations A domain is formalized by a number of formulae, namely: *Action precondition axioms, one for each action *Successor state axioms, one for each fluent *Axioms describing the world in various situations *The foundational axioms of the situation calculus A simple robot world will be modeled as a running example. In this world there is a single robot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frame Problem
In artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic to express facts about a robot in the world. Representing the state of a robot with traditional first-order logic requires the use of many axioms that simply imply that things in the environment do not change arbitrarily. For example, Hayes describes a " block world" with rules about stacking blocks together. In a first-order logic system, additional axioms are required to make inferences about the environment (for example, that a block cannot change position unless it is physically moved). The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, ''Some Philosophical Problems from the Standpoint of Artificial Intelligence''. In this paper, and many that came after, the formal mathematical problem was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Commutative
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Perhaps most familiar as a property of arithmetic, e.g. or , the property can also be used in more advanced settings. The name is needed because there are operations, such as division (mathematics), division and subtraction, that do not have it (for example, ); such operations are ''not'' commutative, and so are referred to as noncommutative operations. The idea that simple operations, such as the multiplication (mathematics), multiplication and addition of numbers, are commutative was for many centuries implicitly assumed. Thus, this property was not named until the 19th century, when new algebraic structures started to be studied. Definition A binary operation * on a Set (mathematics), set ''S'' is ''commutative'' if x * y = y * x for all x,y \in S. An operat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idempotent
Idempotence (, ) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application. The concept of idempotence arises in a number of places in abstract algebra (in particular, in the theory of projectors and closure operators) and functional programming (in which it is connected to the property of referential transparency). The term was introduced by American mathematician Benjamin Peirce in 1870 in the context of elements of algebras that remain invariant when raised to a positive integer power, and literally means "(the quality of having) the same power", from + '' potence'' (same + power). Definition An element x of a set S equipped with a binary operator \cdot is said to be ''idempotent'' under \cdot if : . The ''binary operation'' \cdot is said to be ''idempotent'' if : . Examples * In the monoid (\mathbb, \times) of the natural numbers with multiplication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluent (artificial Intelligence)
In artificial intelligence, a fluent is a condition that can change over time. In logical approaches to reasoning about actions, fluents can be represented in first-order logic by Predicate (logic), predicates having an argument that depends on time. For example, the condition "the box is on the table", if it can change over time, cannot be represented by \mathrm(\mathrm,\mathrm); a third argument is necessary to the predicate \mathrm to specify the time: \mathrm(\mathrm,\mathrm,t) means that the box is on the table at time t. This representation of fluents is modified in the situation calculus by using the sequence of the past actions in place of the current time. A fluent can also be represented by a function, dropping the time argument. For example, that the box is on the table can be represented by on(box,table), where on is a function and not a predicate. In first-order logic, converting predicates to functions is called Reification (knowledge representation), reification; f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frame Problem
In artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic to express facts about a robot in the world. Representing the state of a robot with traditional first-order logic requires the use of many axioms that simply imply that things in the environment do not change arbitrarily. For example, Hayes describes a " block world" with rules about stacking blocks together. In a first-order logic system, additional axioms are required to make inferences about the environment (for example, that a block cannot change position unless it is physically moved). The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, ''Some Philosophical Problems from the Standpoint of Artificial Intelligence''. In this paper, and many that came after, the formal mathematical problem was a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Situation Calculus
The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. The main version of the situational calculus that is presented in this article is based on that introduced by Ray Reiter in 1991. It is followed by sections about McCarthy's 1986 version and a logic programming formulation. Overview The situation calculus represents changing scenarios as a set of first-order logic formulae. The basic elements of the calculus are: *The actions that can be performed in the world *The fluents that describe the state of the world *The situations A domain is formalized by a number of formulae, namely: *Action precondition axioms, one for each action *Successor state axioms, one for each fluent *Axioms describing the world in various situations *The foundational axioms of the situation calculus A simple robot world will be modeled as a running example. In this world there is a single robot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Event Calculus
The event calculus is a logical theory for representing and reasoning about events and about the way in which they change the state of some real or artificial world. It deals both with action events, which are performed by agents, and with external events, which are outside the control of any agent. The event calculus represents the state of the world at any time by the set of all the facts (called '' fluents'') that hold at the time. Events initiate and terminate fluents: The event calculus differs from most other approaches for reasoning about change by reifying time, associating events with the time at which they happen, and associating fluents with the times at which they hold. The original version of the event calculus, introduced by Robert Kowalski and Marek Sergot in 1986, was formulated as a logic program and developed for representing narratives and database updates. Kave Eshghi showed how to use the event calculus for planning, by using abduction to generate hypot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Transactions On Artificial Intelligence
The Royal Swedish Academy of Sciences () is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting natural sciences and mathematics and strengthening their influence in society, whilst endeavouring to promote the exchange of ideas between various disciplines. The goals of the academy are: * To be a forum where researchers meet across subject boundaries, * To offer a unique environment for research, * To provide support to younger researchers, * To reward outstanding research efforts, * To communicate internationally among scientists, * To advance the case for science within society and to influence research policy priorities * To stimulate interest in mathematics and science in school, and * To disseminate and popularize scientific information in various forms. Every year, the academy awards the Nobel Prizes in physics and chemistry, the Sveriges Riksbank Prize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
