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Guarded Logic
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 neither c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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] [Amazon] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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''. It was the first single to feature new bassist John Moyer. Lyrical themes According to vocalist David Draiman, "Guarded" is about how his lifestyle forces him to protect himself emotionally. 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. Vocalist 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." Charts Personnel * David Draiman – vocals * Dan Donegan – guitars, electronics * John Moyer – bass * Mike Wengren Micha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 with close connections to cognitive science and mathematical logic. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 labeled state transition system , where 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 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. Equivalently, is a bisimulatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Modal Logic
Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality, causation. For instance, in epistemic modal logic, the well-formed_formula, formula \Box P can be used to represent the statement that P is known. In deontic modal logic, that same formula can represent that P is a moral obligation. Modal logic considers the inferences that modal statements give rise to. For instance, most epistemic modal logics treat the formula \Box P \rightarrow P as a Tautology_(logic), tautology, representing the principle that only true statements can count as knowledge. However, this formula is not a tautology in deontic modal logic, since what ought to be true can be false. Modal logics are formal systems that include unary operation, unary operators such as \Diamond and \Box, representing possibility and necessi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Temporal Logic
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I eat something"). It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians. Temporal logic has found an important application in formal verification, where it is used to state requirements of hardware or software systems. For instance, one may wish to say that ''whenever'' a request is made, access to a resource is ''eventually'' granted, but it is ''never'' granted to two requestors simultaneously. Such a statement can conveniently be expressed in a temporal logic. Motivation Consider the statement "I am hungry". Though it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Description Logic
Description logics (DL) are a family of formal knowledge representation languages. Many DLs are more expressive than propositional logic but less expressive than first-order logic. In contrast to the latter, the core reasoning problems for DLs are (usually) decidable, and efficient decision procedures have been designed and implemented for these problems. There are general, spatial, temporal, spatiotemporal, and fuzzy description logics, and each description logic features a different balance between expressive power and reasoning complexity by supporting different sets of mathematical constructors. DLs are used in artificial intelligence to describe and reason about the relevant concepts of an application domain (known as ''terminological knowledge''). It is of particular importance in providing a logical formalism for ontologies and the Semantic Web: the Web Ontology Language (OWL) and its profiles are based on DLs. The most notable application of DLs and OWL is in biomedical in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Dynamic Logic (modal Logic)
In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs. A simple example of a statement in dynamic logic is :\text \to text\text, which states that if the ground is currently dry and it rains, then afterwards the ground will be wet. The syntax of dynamic logic contains a language of ''propositions'' (like "the ground is dry") and a language of ''actions'' (like "it rains"). The core modal constructs are , which states that after performing action ''a'' the proposition ''p'' should hold, and \langle a \rangle p, which states that after performing action ''a'' it is possible that ''p'' holds. The action language supports operations a\mathbinb (doing one action followed by another), a \cup b (doing one action or another), and iteration a (doing one action zero or more times). The proposition language supports Boolean operations (and, or, and not). The action logic is expressive enough ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Johan Van Benthem (logician)
Johannes Franciscus Abraham Karel (Johan) van Benthem (born 12 June 1949 in Rijswijk) is a University Professor (') of logic at the University of Amsterdam at the Institute for Logic, Language and Computation and professor of philosophy at Stanford University (at CSLI). He was awarded the Spinozapremie in 1996 and elected a Foreign Fellow of the American Academy of Arts & Sciences in 2015. Biography Van Benthem studied physics ( B.Sc. 1969), philosophy ( M.A. 1972) and mathematics ( M.Sc. 1973) at the University of Amsterdam and received a PhD from the same university under supervision of Martin Löb in 1977. Before becoming University Professor in 2003, he held appointments at the University of Amsterdam (1973–1977), at the University of Groningen (1977–1986), and as a professor at the University of Amsterdam (1986–2003). In 1992 he was elected member of the Royal Netherlands Academy of Arts and Sciences. Van Benthem is known for his research in the area of modal log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
