AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... (1946a, 1946b, 1947) and Rudolf Carnap (1946, 1947) who were the first to formulate axiomatic systems that combined quantification theory with (S5- and S4-type) modal logic. The attempts to interpret quantified modal logic by means of formal semantic methods also began with Carnap (1946, 1947), wher ...
... (1946a, 1946b, 1947) and Rudolf Carnap (1946, 1947) who were the first to formulate axiomatic systems that combined quantification theory with (S5- and S4-type) modal logic. The attempts to interpret quantified modal logic by means of formal semantic methods also began with Carnap (1946, 1947), wher ...
1. Propositional Logic 1.1. Basic Definitions. Definition 1.1. The
... The linear structure of of Hilbert-style deductions, and the very simple list of cases (each step can be only an axiom or an instance of modus ponens) makes it very easy to prove some theorems about Hilbert systems. However these systems are very far removed from ordinary mathematics, and they don’t ...
... The linear structure of of Hilbert-style deductions, and the very simple list of cases (each step can be only an axiom or an instance of modus ponens) makes it very easy to prove some theorems about Hilbert systems. However these systems are very far removed from ordinary mathematics, and they don’t ...
Acts of Commanding and Changing Obligations
... are here trying to capture the effects of commands, and commands can be, and usually are, given to some specific addressees. In order to capture how such commands work in a situation where their addressees and non-addressees are present, it is necessary to work with a collection of accessibility rel ...
... are here trying to capture the effects of commands, and commands can be, and usually are, given to some specific addressees. In order to capture how such commands work in a situation where their addressees and non-addressees are present, it is necessary to work with a collection of accessibility rel ...
Algebraic foundations for the semantic treatment of inquisitive content
... in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, ...
... in a satisfactory way, should be defined as non-empty, downward closed sets of possibilities, where each possibility in turn is a set of possible worlds. We define a natural entailment order over such propositions, capturing when one proposition is at least as informative and inquisitive as another, ...
Introduction to Linear Logic - Shane Steinert
... The idea is that a proof structure with conclusions A1 , . . . , An in fact proves A1 ` · · · ` An . As defined, proof structures can be well-formed even if the associated ` is not provable. ...
... The idea is that a proof structure with conclusions A1 , . . . , An in fact proves A1 ` · · · ` An . As defined, proof structures can be well-formed even if the associated ` is not provable. ...
Propositional logic - Cheriton School of Computer Science
... departure between schools of logical thought, and the choice we make fundamentally affects the properties of the resulting logic. If we believe that ¬φ means that φ is false, then we are classicists and our proof theory becomes a proof theory for classical logic. We will then handle negation in a wa ...
... departure between schools of logical thought, and the choice we make fundamentally affects the properties of the resulting logic. If we believe that ¬φ means that φ is false, then we are classicists and our proof theory becomes a proof theory for classical logic. We will then handle negation in a wa ...
Interactive Theorem Proving with Temporal Logic
... These readings will be reected directly in the generation of text from proofs. Most of the propositional rules are straightforward. The ^ right rule for example states that if A and B each hold from the assumptions , then we can conclude A ^ B holds under the same assumptions. Many of the readings ...
... These readings will be reected directly in the generation of text from proofs. Most of the propositional rules are straightforward. The ^ right rule for example states that if A and B each hold from the assumptions , then we can conclude A ^ B holds under the same assumptions. Many of the readings ...
Logic and Proof Jeremy Avigad Robert Y. Lewis Floris van Doorn
... One can adopt another view of logic, however, as a system where some symbols have a fixed meaning, such as the symbols for “and,” “or,” and “not,” and others have a meaning that is taken to vary. For example, the expression P ∧ (Q ∨ R), read “P and either Q or R,” may be true or false depending on th ...
... One can adopt another view of logic, however, as a system where some symbols have a fixed meaning, such as the symbols for “and,” “or,” and “not,” and others have a meaning that is taken to vary. For example, the expression P ∧ (Q ∨ R), read “P and either Q or R,” may be true or false depending on th ...
Default reasoning using classical logic
... and 5 we discuss how the models presented in Section 3 can be treated as classical models of propositional logic. We present algorithms that associate for each nite default theory a classical propositional theory that characterizes its extensions. Then, in Section 6 we use constraint satisfaction t ...
... and 5 we discuss how the models presented in Section 3 can be treated as classical models of propositional logic. We present algorithms that associate for each nite default theory a classical propositional theory that characterizes its extensions. Then, in Section 6 we use constraint satisfaction t ...
Informal Proceedings of the 30th International Workshop on
... protocol for key exchange and then encryption with derived keys. For human users this is most visible as transport layer security (TLS) used by all web browsers. History has shown that developing such protocols is an error-prone process, and attacks have been found even after protocols were in wides ...
... protocol for key exchange and then encryption with derived keys. For human users this is most visible as transport layer security (TLS) used by all web browsers. History has shown that developing such protocols is an error-prone process, and attacks have been found even after protocols were in wides ...
Towards an Epistemic Logic of Grounded Belief
... knowledge alone, however this knowledge has historically been very difficult to characterize. Finally, I turn to motivating the last part of the definition, Def. 2.1.1(c). Def. 2.1.1(c) states that an ideal agent cannot posses knowledge of falsity. For any situation it seems strange to say that one ...
... knowledge alone, however this knowledge has historically been very difficult to characterize. Finally, I turn to motivating the last part of the definition, Def. 2.1.1(c). Def. 2.1.1(c) states that an ideal agent cannot posses knowledge of falsity. For any situation it seems strange to say that one ...
The Foundations
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
The Foundations
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
Here - Dorodnicyn Computing Centre of the Russian Academy of
... Thus, from the main Cantor's theorem it follows that the Cantor's axiomatic statement "all sets are actual" (above) - which is the only basis for all his transfinite ordinal and cardinal constructions is wrong, i.e., according to Poincare, all Cantor's set theory as well as all modern "non-naive" ax ...
... Thus, from the main Cantor's theorem it follows that the Cantor's axiomatic statement "all sets are actual" (above) - which is the only basis for all his transfinite ordinal and cardinal constructions is wrong, i.e., according to Poincare, all Cantor's set theory as well as all modern "non-naive" ax ...
chapter9
... • Since any subset has a maximum depth of nesting in terms, we can find the subset by generating all instantiations with constant symbols, then all with depth 1, and so on ...
... • Since any subset has a maximum depth of nesting in terms, we can find the subset by generating all instantiations with constant symbols, then all with depth 1, and so on ...
thèse - IRIT
... the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D- ...
... the truth value of a propositional variable here or there, if possible. These atomic programs are then combined by the usual dynamic logic connectives. The resulting formalism is called dynamic here-and-there logic (D-HT), and it allows for atomic change of equilibrium models. Moreover, we relate D- ...
Refinement Modal Logic
... generality, and also applied to the multi-agent case. Previous works [19, 37] employed a notion of refinement. In [37] it was shown that model restrictions were not sufficient to simulate informative events, and they introduced refinement trees for this purpose — a precursor of the dynamic epistemic ...
... generality, and also applied to the multi-agent case. Previous works [19, 37] employed a notion of refinement. In [37] it was shown that model restrictions were not sufficient to simulate informative events, and they introduced refinement trees for this purpose — a precursor of the dynamic epistemic ...
Topological aspects of real-valued logic
... Chapter 4, which contains material from the joint papers [38], [39], and [40], is devoted to developing the model theory of commutative unital C*-algebras. In this chapter we work primarily in continuous first-order logic, though we also make brief use of the logic developed in Chapter 3. As mention ...
... Chapter 4, which contains material from the joint papers [38], [39], and [40], is devoted to developing the model theory of commutative unital C*-algebras. In this chapter we work primarily in continuous first-order logic, though we also make brief use of the logic developed in Chapter 3. As mention ...
A Logical Framework for Default Reasoning
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
... instance of these can be used as a hypothesis if it is consistent. Definition 1 a scenario of F, ∆ is a set D ∪ F where D is a set of ground instances of elements of ∆ such that D ∪ F is consistent. Definition 2 If g is a closed formula then an explanation of g from F, ∆ is a scenario of F, ∆ which ...
Continuous Markovian Logic – From Complete ∗ Luca Cardelli
... where L is the set of logical formulas. However, the computability of D is sometimes problematic, as it is the computability of d(P, φ) for an infinite or extremely big process P and for this reason approximation techniques such as statistical model checking [15, 22] are used to evaluate d(P, φ) wit ...
... where L is the set of logical formulas. However, the computability of D is sometimes problematic, as it is the computability of d(P, φ) for an infinite or extremely big process P and for this reason approximation techniques such as statistical model checking [15, 22] are used to evaluate d(P, φ) wit ...
The substitutional theory of logical consequence
... If logical truth is understood as truth under all interpretations, then it is an oddity of the model-theoretic account that there is not a special interpretation of a given sentence that allows one to understand the sentence at face value. Several philosophers and logicians have felt the need for su ...
... If logical truth is understood as truth under all interpretations, then it is an oddity of the model-theoretic account that there is not a special interpretation of a given sentence that allows one to understand the sentence at face value. Several philosophers and logicians have felt the need for su ...
Understanding SPKI/SDSI Using First-Order Logic
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
... An identifier is a word over some given standard alphabet. The set of all identifiers is denoted by A, and an identifier is denoted by A or B (often with subscripts). We assume that both K and A are countable. We do not consider SDSI 1.1 [30] special roots, which are identifiers that are bound to th ...
Section 1: Propositional Logic
... You may wonder why we’re concerned with statement forms since we’re not concerned with function forms in other areas of mathematics but just their values. That is a misconception. We are concerned with function forms in algebra. It’s just that you’re so used to the equality of different forms that y ...
... You may wonder why we’re concerned with statement forms since we’re not concerned with function forms in other areas of mathematics but just their values. That is a misconception. We are concerned with function forms in algebra. It’s just that you’re so used to the equality of different forms that y ...
The Foundations
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
... Two syntactically (i.e., textually) different compound propositions may be semantically identical (i.e., have the same meaning). We call them equivalent. Learn: Various equivalence rules or laws. How to prove equivalences using symbolic derivations. Analogy: x * (5 + y) and xy + 5x are alway ...
Equivalence for the G3'-stable models semantics
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...
... which two programs are strongly G03 -equivalent also guarantee that two disjunctive programs are strongly equivalent in the p-stable semantics. We present two main results that guarantee G03 strong equivalence, one for two arbitrary programs and another one for a couple of programs of the form P , P ...