Refinement Modal Logic
... refinement trees for this purpose — a precursor of the dynamic epistemic logics developed later (for an overview, see [57]). This usage of refinement as a more general operation than model restriction is similar to ours. In formal methods literature, see e.g. [62], refinement of datatypes is conside ...
... refinement trees for this purpose — a precursor of the dynamic epistemic logics developed later (for an overview, see [57]). This usage of refinement as a more general operation than model restriction is similar to ours. In formal methods literature, see e.g. [62], refinement of datatypes is conside ...
Introduction to Modal and Temporal Logic
... Goal: Deducibility captures logical consequence via syntax manipulation. Introduction to Modal and Temporal Logics ...
... Goal: Deducibility captures logical consequence via syntax manipulation. Introduction to Modal and Temporal Logics ...
Modal Languages and Bounded Fragments of Predicate Logic
... What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has b ...
... What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has b ...
doc
... Explanation: Clearly xFx is false in this case, since there are numbers that are not prime, for example 6. So, then xFx→xGx is true. Now, note that x(Fx→Gx) is false since there is a number n such that ~(Fn→Gn), for example 5. So, the above interpretation shows that the sequent is invalid. ...
... Explanation: Clearly xFx is false in this case, since there are numbers that are not prime, for example 6. So, then xFx→xGx is true. Now, note that x(Fx→Gx) is false since there is a number n such that ~(Fn→Gn), for example 5. So, the above interpretation shows that the sequent is invalid. ...
Logic 1 Lecture Notes Part I: Propositional Logic
... language. So they are variables of our meta-language, used to make statements of generality, and hence are called “meta-variables”. Roughly speaking, when we say “Let A be a formula …”, then this is a way of referring generally to any arbitrary formula, such as ¬P, P ∨ Q, (P ∧ Q) → P, etc. This is c ...
... language. So they are variables of our meta-language, used to make statements of generality, and hence are called “meta-variables”. Roughly speaking, when we say “Let A be a formula …”, then this is a way of referring generally to any arbitrary formula, such as ¬P, P ∨ Q, (P ∧ Q) → P, etc. This is c ...
THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL
... Shehtman [13]. Still, from a philosophical point of view this semantics left much to be desired. The introduction of counterpart relations — although in line with at least some philosophical ideas, notably by Lewis — is not always very satisfactory since it makes the notion of an object a derived on ...
... Shehtman [13]. Still, from a philosophical point of view this semantics left much to be desired. The introduction of counterpart relations — although in line with at least some philosophical ideas, notably by Lewis — is not always very satisfactory since it makes the notion of an object a derived on ...
X - UOW
... In constructing a truth table for a compound statement comprised of n statements, there will be 2n combinations of truth values. This method can be long for large numbers of statements. We will consider a quicker method for determining if a compound statement is a tautology. However, truth tables ar ...
... In constructing a truth table for a compound statement comprised of n statements, there will be 2n combinations of truth values. This method can be long for large numbers of statements. We will consider a quicker method for determining if a compound statement is a tautology. However, truth tables ar ...
Strong Completeness for Iteration
... where T is an Set-functor, and η : Id ⇒ T (unit) and µ : T 2 ⇒ T (multiplication) are natural transformations that satisfy the following coherence laws: µ ◦ ηT = µ ◦ T η = id T and µ ◦ µT = µ ◦ T µ. For a Set-monad T = (T, η, µ), the Kleisli category K`(T) has sets as objects and functions X → T Y a ...
... where T is an Set-functor, and η : Id ⇒ T (unit) and µ : T 2 ⇒ T (multiplication) are natural transformations that satisfy the following coherence laws: µ ◦ ηT = µ ◦ T η = id T and µ ◦ µT = µ ◦ T µ. For a Set-monad T = (T, η, µ), the Kleisli category K`(T) has sets as objects and functions X → T Y a ...
MODAL LANGUAGES AND BOUNDED FRAGMENTS OF
... and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment ...
... and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) As a counterproposal, then, we define a large fragment of predicate logic characterized by its use of only bounded quantification. This so-called guarded fragment ...
Reasoning about Action and Change
... in the planning literature (see Pnueli, 1981; Manna et al., 1993). The rest of the paper is organized as follows. In Section 2, PDL is introduced together with a reminder of the basic steps of its completeness proof. Section 3 shows that PDL may be modified in order to deal with multiagent domains i ...
... in the planning literature (see Pnueli, 1981; Manna et al., 1993). The rest of the paper is organized as follows. In Section 2, PDL is introduced together with a reminder of the basic steps of its completeness proof. Section 3 shows that PDL may be modified in order to deal with multiagent domains i ...
The Logic of Provability
... Similarly, t < t0 is ∆ for any terms t, t0 . Note further that the class of ∆ formulas is closed under negation and conjunction: the negation of a ∆ formula is always a ∆ formula and the conjunction of two ∆ formulas is itself a ∆ formula. With these in hand, it follows easily that the ∆ formulas ar ...
... Similarly, t < t0 is ∆ for any terms t, t0 . Note further that the class of ∆ formulas is closed under negation and conjunction: the negation of a ∆ formula is always a ∆ formula and the conjunction of two ∆ formulas is itself a ∆ formula. With these in hand, it follows easily that the ∆ formulas ar ...
7 LOGICAL AGENTS
... The central component of a knowledge-based agent is its knowledge base, or KB. A knowledge base is a set of sentences. (Here “sentence” is used as a technical term. It is related but not identical to the sentences of English and other natural languages.) Each sentence is expressed in a language call ...
... The central component of a knowledge-based agent is its knowledge base, or KB. A knowledge base is a set of sentences. (Here “sentence” is used as a technical term. It is related but not identical to the sentences of English and other natural languages.) Each sentence is expressed in a language call ...
One-dimensional Fragment of First-order Logic
... (cf. the formulae PreCons δ and Cons δ in Section 4.1). This way we can encode information concerning accessibility relations by using formulae of MFO. This construction does not work if one tries to maximize both a binary relation R and its complement R at the same time: the problem is that the max ...
... (cf. the formulae PreCons δ and Cons δ in Section 4.1). This way we can encode information concerning accessibility relations by using formulae of MFO. This construction does not work if one tries to maximize both a binary relation R and its complement R at the same time: the problem is that the max ...
Deep Sequent Systems for Modal Logic
... modalities but also variables and an accessibility relation. There are some concerns about incorporating the semantics into the syntax of a proof system in this way. Avron discusses them in [1], for example. However, even without these concerns, it still is an interesting question whether we can for ...
... modalities but also variables and an accessibility relation. There are some concerns about incorporating the semantics into the syntax of a proof system in this way. Avron discusses them in [1], for example. However, even without these concerns, it still is an interesting question whether we can for ...
19_pl
... If a problem domain can be represented formally, then a decision maker can use logical reasoning to make rational decisions Many types of logic Propositional Logic (Boolean logic) First-Order Logic (aka first-order predicate calculus) Non-Monotonic Logic Markov Logic A logic includes: synt ...
... If a problem domain can be represented formally, then a decision maker can use logical reasoning to make rational decisions Many types of logic Propositional Logic (Boolean logic) First-Order Logic (aka first-order predicate calculus) Non-Monotonic Logic Markov Logic A logic includes: synt ...
Propositional Logic
... [Partially based on slides from Jerry Zhu, Louis Oliphant and Andrew Moore] ...
... [Partially based on slides from Jerry Zhu, Louis Oliphant and Andrew Moore] ...
Introduction to Formal Logic - Web.UVic.ca
... This inference fulfils condition (i): there is no possible case where its premises could be true and its conclusion false. Hence the inference is valid. But the inference also fulfils condition (ii), because its premises are true: all whales are in fact mammals, and all mammals have spinal chords. N ...
... This inference fulfils condition (i): there is no possible case where its premises could be true and its conclusion false. Hence the inference is valid. But the inference also fulfils condition (ii), because its premises are true: all whales are in fact mammals, and all mammals have spinal chords. N ...
Deep Sequent Systems for Modal Logic
... However, there are concerns about incorporating the semantics into the syntax of a proof system, see for example [1]. For motivating the present work I would just like to take it as a given that it is an interesting question whether something that has been achieved using labels can also be achieved ...
... However, there are concerns about incorporating the semantics into the syntax of a proof system, see for example [1]. For motivating the present work I would just like to take it as a given that it is an interesting question whether something that has been achieved using labels can also be achieved ...
A modal perspective on monadic second
... finite directed graphs. The precise definition of strong first-order reductions (found in [18]) is of no particular importance for the present paper, as we give a virtually self-contained exposition of all our results. As a by-product of our investigations we obtain a simple, effective procedure (in ...
... finite directed graphs. The precise definition of strong first-order reductions (found in [18]) is of no particular importance for the present paper, as we give a virtually self-contained exposition of all our results. As a by-product of our investigations we obtain a simple, effective procedure (in ...
1992-Ideal Introspective Belief
... derivable from the premises alone. For example, consider the premise set {lLp > q,p V q}. We would like since there is no reasonable way of to conclude ‘Lp, coming to believe p. But an inference rule that would allow us to conclude 1Lp would have to take into account all possible derivations, includ ...
... derivable from the premises alone. For example, consider the premise set {lLp > q,p V q}. We would like since there is no reasonable way of to conclude ‘Lp, coming to believe p. But an inference rule that would allow us to conclude 1Lp would have to take into account all possible derivations, includ ...