a basis for a mathematical theory of computation
... of information. The present paper contains no information about this. The present paper is divided into two sections. The first contains several descriptive formalisms with a few examples of their use, and the second contains what little theory we have that enables us to prove the equivalence of com ...
... of information. The present paper contains no information about this. The present paper is divided into two sections. The first contains several descriptive formalisms with a few examples of their use, and the second contains what little theory we have that enables us to prove the equivalence of com ...
1. the language of mathematics
... In order to communicate effectively, people must agree on the meanings of certain words and phrases. When there is ambiguity, confusion can result. Consider the following conversation in a car at a noisy intersection: Carol: “Turn left!” Bob: “I didn’t hear you. Left?” Carol: “Right!” Question: Whic ...
... In order to communicate effectively, people must agree on the meanings of certain words and phrases. When there is ambiguity, confusion can result. Consider the following conversation in a car at a noisy intersection: Carol: “Turn left!” Bob: “I didn’t hear you. Left?” Carol: “Right!” Question: Whic ...
Justification logic with approximate conditional probabilities
... t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemov [1] with the aim of giving a classical provability interpretation for the modal logic S4 and hence also for intuitionistic logic. The Logic of Proofs interprets justification terms as formal proof ...
... t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemov [1] with the aim of giving a classical provability interpretation for the modal logic S4 and hence also for intuitionistic logic. The Logic of Proofs interprets justification terms as formal proof ...
Integrating Logical Reasoning and Probabilistic Chain Graphs
... Furthermore, we can associate weights to the assumables according to the potential functions. For instance, weight(ϕCD (t, t) : 18, ϕCD (t, f ) : 2, ϕCD (f, t) : 5, ϕCD (f, f ) : 2) In order to be able to probabilistically interpret a CL theory T , a number of assumptions are added to those of abduc ...
... Furthermore, we can associate weights to the assumables according to the potential functions. For instance, weight(ϕCD (t, t) : 18, ϕCD (t, f ) : 2, ϕCD (f, t) : 5, ϕCD (f, f ) : 2) In order to be able to probabilistically interpret a CL theory T , a number of assumptions are added to those of abduc ...
A Simple Tableau System for the Logic of Elsewhere
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
Page references correspond to locations of Extra Ex
... There are various ways to answer this question, depending on the universe. If we take as our universe all freshmen at the College and use the predicate T (x) to mean “x is taking CS 101”, then the statement can be written as ∀x T (x). However, we may wish to use the universe of all students at the C ...
... There are various ways to answer this question, depending on the universe. If we take as our universe all freshmen at the College and use the predicate T (x) to mean “x is taking CS 101”, then the statement can be written as ∀x T (x). However, we may wish to use the universe of all students at the C ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... Hilbert and wanted to reason about sequents in a finitistic way.) Because of the compactness property, which syntactical consequence relations usually have, this is not such an essential limitation. But, in general, it makes sense to extend Gentzen’s approach to sequents ├ A with infinite. Most ...
... Hilbert and wanted to reason about sequents in a finitistic way.) Because of the compactness property, which syntactical consequence relations usually have, this is not such an essential limitation. But, in general, it makes sense to extend Gentzen’s approach to sequents ├ A with infinite. Most ...
- Horn-Representation of a Concept Lattice,
... select those that are Horn, and their conjunction is exactly the Horn representation FK . However, there are several complexity results from propositional logic that imply limitations for the practical implementation of such a procedure. From a result shown in [12] it follows that there exist contex ...
... select those that are Horn, and their conjunction is exactly the Horn representation FK . However, there are several complexity results from propositional logic that imply limitations for the practical implementation of such a procedure. From a result shown in [12] it follows that there exist contex ...
duality of quantifiers ¬8xA(x) 9x¬A(x) ¬9xA(x) 8x¬A(x)
... if C is ⊥ then output “unsatisfiable” else add C to S This is not an algorithm because we haven’t said how to make choices, and there is no point at which we decide “satisfiable”. ...
... if C is ⊥ then output “unsatisfiable” else add C to S This is not an algorithm because we haven’t said how to make choices, and there is no point at which we decide “satisfiable”. ...
Quantitative Temporal Logics: PSPACE and below - FB3
... ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following, we reduce satisfiability of QTLb formulas to the satisfiability of QTL1 -formula, i.e., QTLformulas in which all upper interval bounds have value 1. As the coding of numbers is not an issue in the latter lo ...
... ϕ, where J is obtained from I by replacing the upper interval bound n by 1. In the following, we reduce satisfiability of QTLb formulas to the satisfiability of QTL1 -formula, i.e., QTLformulas in which all upper interval bounds have value 1. As the coding of numbers is not an issue in the latter lo ...
Nonmonotonic Reasoning - Computer Science Department
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
... by usual type reasoning systems, except that the rules carry the list of “exceptional cases” making the application of such rule invalid. Formally, Reiter, [25] introduced the concept of default theory. A default theory is a pair hD, W i where W is a set of sentences of the underlying language L and ...
Ultrasheaves
... First in this section we give a background in categorical logic and general topos theory. Then follows a background directly related to ultrasheaves. 1.1. Background in categorical logic. The study of sheaf theory was pioneered by Grothendieck. He was motivated by examples of sheaves in algebraic ge ...
... First in this section we give a background in categorical logic and general topos theory. Then follows a background directly related to ultrasheaves. 1.1. Background in categorical logic. The study of sheaf theory was pioneered by Grothendieck. He was motivated by examples of sheaves in algebraic ge ...
Workshop5. Logic in Language
... agree with your mini-terms in the above table. (i) Build two simulated digital circuits, one for the expression given in (h) and the second for your simplified expression in (h). Check that both give identical results. (j) Write code for both expressions and test that they too have identical behavio ...
... agree with your mini-terms in the above table. (i) Build two simulated digital circuits, one for the expression given in (h) and the second for your simplified expression in (h). Check that both give identical results. (j) Write code for both expressions and test that they too have identical behavio ...