Modal logic and the approximation induction principle
... from the richest characterizations, which correspond to the canonical process equivalences, there are also finitary versions (denoted with a superscript ∗ ), which allow only conjunctions over a finite set. Intermediate equivalences based on formulas with arbitrary conjunctions but of finite depth a ...
... from the richest characterizations, which correspond to the canonical process equivalences, there are also finitary versions (denoted with a superscript ∗ ), which allow only conjunctions over a finite set. Intermediate equivalences based on formulas with arbitrary conjunctions but of finite depth a ...
Non-Classical Logic
... Together these results entail the equivalence of semantic the formula false, so it must be logically valid. and deductive validity. The same process can be used to show that a formula Proofs of these results with Priest’s tableaux method of isn’t logically valid if the process continues until the en ...
... Together these results entail the equivalence of semantic the formula false, so it must be logically valid. and deductive validity. The same process can be used to show that a formula Proofs of these results with Priest’s tableaux method of isn’t logically valid if the process continues until the en ...
Introduction to Modal Logic - CMU Math
... then w1 “knows about” w2 and must consider it in making decisions about whether something is possible or necessary. V is a function mapping the set of propositional variables P to P(W ). The interpretation is the if P is mapped into a set contain w then w thinks that the variable P is true. ...
... then w1 “knows about” w2 and must consider it in making decisions about whether something is possible or necessary. V is a function mapping the set of propositional variables P to P(W ). The interpretation is the if P is mapped into a set contain w then w thinks that the variable P is true. ...
Paper - Department of Computer Science and Information Systems
... S4, S4.3. The computational complexity of the admissibility problem for these logics has been investigated in [Jerabek 2007]. For example, for intuitionistic logic, S4, and GL, the problem was shown to be NExpTime-complete. For further studies on unification and admissibility of rules in intuitionis ...
... S4, S4.3. The computational complexity of the admissibility problem for these logics has been investigated in [Jerabek 2007]. For example, for intuitionistic logic, S4, and GL, the problem was shown to be NExpTime-complete. For further studies on unification and admissibility of rules in intuitionis ...
The Expressive Power of Modal Dependence Logic
... Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , ...
... Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , ...
Section 1: Propositional Logic
... “look different.” They are the same if they “look the same.” This is not very precise, but is good enough. Thus, for example, p∨q and q ∨p look different and so are different statement forms. We say that two statement forms are logically equivalent (or simply equivalent) if they have the same truth ...
... “look different.” They are the same if they “look the same.” This is not very precise, but is good enough. Thus, for example, p∨q and q ∨p look different and so are different statement forms. We say that two statement forms are logically equivalent (or simply equivalent) if they have the same truth ...
Label-free Modular Systems for Classical and Intuitionistic Modal
... logics but some coincide, such that there are only 15, which can be arranged in a cube as shown in Figure 2. This cube has the same shape in the classical as well as in the intuitionistic setting. However, the two papers [2] and [18] have one drawback: Although they provide cut-free systems for all ...
... logics but some coincide, such that there are only 15, which can be arranged in a cube as shown in Figure 2. This cube has the same shape in the classical as well as in the intuitionistic setting. However, the two papers [2] and [18] have one drawback: Although they provide cut-free systems for all ...
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 ...
pdf
... elements. Moreover, they take awareness with respect to domain elements, not formulas; that is, agents are (un)aware of objects (i.e., domain elements), not formulas. They also allow different domains at different worlds; more precisely, they allow an agent to have a subjective view of what the set ...
... elements. Moreover, they take awareness with respect to domain elements, not formulas; that is, agents are (un)aware of objects (i.e., domain elements), not formulas. They also allow different domains at different worlds; more precisely, they allow an agent to have a subjective view of what the set ...
Logic for Computer Science. Lecture Notes
... Logical formalisms are applied in many areas of computer science. The extensive use of those formalisms resulted in defining hundreds of logics that fit nicely to particular application areas. Let us then first clarify what do we mean by a logic. Recall first the rôle of logic in the clarification of hu ...
... Logical formalisms are applied in many areas of computer science. The extensive use of those formalisms resulted in defining hundreds of logics that fit nicely to particular application areas. Let us then first clarify what do we mean by a logic. Recall first the rôle of logic in the clarification of hu ...
cl-ch9
... denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two distinct elements, but false if it has only one.) Closed formulas, which are a ...
... denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two distinct elements, but false if it has only one.) Closed formulas, which are a ...
Algebraizing Hybrid Logic - Institute for Logic, Language and
... on at least one branch of the tableau will be satisfiable by label too. Remark 2.4.2. The systematic tableau construction is defined in [5]. Roughly speaking, this construction is needed in order to prove strong completeness. Theorem 2.4.1. ([5]) Any consistent set of formulas in countable language ...
... on at least one branch of the tableau will be satisfiable by label too. Remark 2.4.2. The systematic tableau construction is defined in [5]. Roughly speaking, this construction is needed in order to prove strong completeness. Theorem 2.4.1. ([5]) Any consistent set of formulas in countable language ...
article - British Academy
... embed in the same way-and if Godel’s result is provable by manipulation of one of them, it doesn’t follow that his result is provable by manipulation of the other. Suppose my system is the F and that I can prove that I cannot prove that 0 = 1. Then the F can prove that I cannot prove that 0 = 1. It ...
... embed in the same way-and if Godel’s result is provable by manipulation of one of them, it doesn’t follow that his result is provable by manipulation of the other. Suppose my system is the F and that I can prove that I cannot prove that 0 = 1. Then the F can prove that I cannot prove that 0 = 1. It ...
34-2.pdf
... We would like to extend the language to describe interactions between processes, but first we need to explain what we mean by process interaction. Two processes interact when one sends information and the other receives it. We formalize this notion, by creating pairs of actions. Each pair consists o ...
... We would like to extend the language to describe interactions between processes, but first we need to explain what we mean by process interaction. Two processes interact when one sends information and the other receives it. We formalize this notion, by creating pairs of actions. Each pair consists o ...
Strong Completeness and Limited Canonicity for PDL
... The obvious idea would be to apply the Henkin construction of a canonical model from maximal consistent sets of formulas, and to prove Lindenbaum’s Lemma for PDLω that every consistent set can be extended to a maximal consistent set. The last part is problematic: the limit construction in Lindenbaum ...
... The obvious idea would be to apply the Henkin construction of a canonical model from maximal consistent sets of formulas, and to prove Lindenbaum’s Lemma for PDLω that every consistent set can be extended to a maximal consistent set. The last part is problematic: the limit construction in Lindenbaum ...
Deciding Intuitionistic Propositional Logic via Translation into
... Fp special , iff op(Fp ) ∈ {⇒, ¬} and pol(Fp ) = 0. In the above example we obtain W(F ) = {w, w111 , w121 }. The respective subformulas appear boxed in fig. 3. Recall that the elements wp of W(F ) denote functions which map a given knowledge stage w to an accessible one w∗ refuting Fp . For fig. 2 ...
... Fp special , iff op(Fp ) ∈ {⇒, ¬} and pol(Fp ) = 0. In the above example we obtain W(F ) = {w, w111 , w121 }. The respective subformulas appear boxed in fig. 3. Recall that the elements wp of W(F ) denote functions which map a given knowledge stage w to an accessible one w∗ refuting Fp . For fig. 2 ...
Truth-Functional Propositional Logic
... Or, also designated Disjunction, is represented by a ∨ (vel or wedge). The components of a disjunction A∨B are called its disjuncts, and the disjunction is stipulated to be true if and only if either one of its disjuncts are true, that is, if and only if at least one of its disjuncts is true. Going ...
... Or, also designated Disjunction, is represented by a ∨ (vel or wedge). The components of a disjunction A∨B are called its disjuncts, and the disjunction is stipulated to be true if and only if either one of its disjuncts are true, that is, if and only if at least one of its disjuncts is true. Going ...
