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Guarded Fragment
Guarded logic is a choice set of dynamic logic involved in choices, where outcomes are limited. A simple example of guarded logic is as follows: if X is true, then Y, else Z can be expressed in dynamic logic as (X?;Y)∪(~X?;Z). This shows a guarded logical choice: if X holds, then X?;Y is equal to Y, and ~X?;Z is blocked, and Y∪block is also equal to Y. Hence, when X is true, the primary performer of the action can only take the Y branch, and when false the Z branch. A real-world example is the idea of paradox: something cannot be both true and false. A guarded logical choice is one where any change in true affects all decisions made down the line. History Before the use of guarded logic there were two major terms used to interpret modal logic. Mathematical logic and database theory (Artificial Intelligence) were first-order predicate logic. Both terms found sub-classes of first-class logic and efficiently used in solvable languages which can be used for research. But neithe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Choice Set
A choice set is a finite collection of available options selected from a larger theoretical decision space. For example, a consumer has thousands of conceivable alternatives when purchasing a car, far more than they could reasonably be expected to evaluate. As such they will often narrow their search to only vehicles of a certain make, or within a specific price range. By reducing the choice set to a manageable number of alternatives, people are able to make complex decisions between theoretically infinite alternatives in a practical time frame. Choice sets are often used in psychological and market research to make data collection and evaluation more manageable, or to make direct comparisons between a specific set of choices. Choice task The respondent is asked a choice task. Usually this is which of the alternatives they prefer. In this example, the Choice task is ' forced'. An 'unforced' choice would allow the respondents to also select 'Neither'. The choice task is used as the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guarded Second-Order Logic
"Guarded" is a song by American heavy metal band Disturbed. It was released on June 28, 2005, as a promotional single for their third studio album, ''Ten Thousand Fists''. "Guarded" was the first single featuring their new bassist John Moyer. The track is featured in the soundtrack of the film ''Saw III'', and on the video game soundtrack of '' MX vs. ATV Untamed''. Lyrical themes According to vocalist David Draiman, "Guarded" is about how his lifestyle forces him to guard himself. He said, "It's a song that reflects what choosing this life forces certain people to do in a certain way — you have to remain guarded on a certain level." Release "Guarded" was released to radio stations as a promotional single on June 28, 2005. David Draiman said, "he songwas put out there to just whet everybody's appetite. It's one of the more aggressive tracks on the record, just to remind everybody where we came from and who we are. Kind of give back to the core a little bit." Chart position ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automata Theory
Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματος, which means "self-acting, self-willed, self-moving". An automaton (automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically. An automaton with a finite number of states is called a Finite Automaton (FA) or Finite-State Machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows). As the automaton sees a symbol of input, it makes a transition (or jump) to another state, according to its transition function, which takes the previous state and current input symbol as its arguments. Automata the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bisimulation
In theoretical computer science a bisimulation is a binary relation between state transition systems, associating systems that behave in the same way in that one system simulates the other and vice versa. Intuitively two systems are bisimilar if they, assuming we view them as playing a ''game'' according to some rules, match each other's moves. In this sense, each of the systems cannot be distinguished from the other by an observer. Formal definition Given a labelled state transition system (S, \Lambda, →), where S is a set of states, \Lambda is a set of labels and → is a set of labelled transitions (i.e., a subset of S \times \Lambda \times S), a bisimulation is a binary relation R \subseteq S \times S, such that both R and its converse R^T are simulations. From this follows that the symmetric closure of a bisimulation is a bisimulation, and that each symmetric simulation is a bisimulation. Thus some authors define bisimulation as a symmetric simulation. Equivalen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a '' possible world''. A formula's truth value ... [...More Info...] |
