a semantic perspective - Institute for Logic, Language and
... chapters in this handbook. Thus the reader will find here definitions and discussions of all the basic tools needed in modal model theory (such as the standard translation, generated submodels, bounded morphisms, and so on). Basic results about these concepts are stated and some simple proofs are gi ...
... chapters in this handbook. Thus the reader will find here definitions and discussions of all the basic tools needed in modal model theory (such as the standard translation, generated submodels, bounded morphisms, and so on). Basic results about these concepts are stated and some simple proofs are gi ...
5 model theory of modal logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related to ...
Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Logic in Nonmonotonic Reasoning
... one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into account when combined with the inertia assumption, since they override the latter. The ramification problem has raised general questions on the nature of caus ...
... one lock produces an indirect effect of opening the suitcase if and only if the other lock is open. Such derived effects should be taken into account when combined with the inertia assumption, since they override the latter. The ramification problem has raised general questions on the nature of caus ...
Artificial Intelligence
... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...
... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...
Classical Propositional Logic
... Completeness A Henkin-style Completeness Proof for Natural Deduction Computability ...
... Completeness A Henkin-style Completeness Proof for Natural Deduction Computability ...
Ground Nonmonotonic Modal Logics - Dipartimento di Informatica e
... Recently, there have been a number of attempts to reconcile fix-point and semantic characterizations of modal nonmonotonic logics. In particular, Schwarz [30] proposed a semantics for McDermott and Doyle’s logics. However, the notion of minimal knowledge underlying the above cited works is stronger ...
... Recently, there have been a number of attempts to reconcile fix-point and semantic characterizations of modal nonmonotonic logics. In particular, Schwarz [30] proposed a semantics for McDermott and Doyle’s logics. However, the notion of minimal knowledge underlying the above cited works is stronger ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... The paper is organized as follows. In Section 2, we present and discuss von Wright’s original work in preference logic, in order to motivate some of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal ...
... The paper is organized as follows. In Section 2, we present and discuss von Wright’s original work in preference logic, in order to motivate some of the notions we develop later, but also as a foundational standard against which we can evaluate our own results. In Section 3, we present a basic modal ...
relevance logic - Consequently.org
... is that relevance logicians by and large believe we are using ‘implies’ in the ordinary non-technical sense, in which a sentence like (3) might be true without there being any logical (or even necessary) implication from ‘Today is Tuesday’ to ‘This is Belgium’. Relevance logicians are not themselves ...
... is that relevance logicians by and large believe we are using ‘implies’ in the ordinary non-technical sense, in which a sentence like (3) might be true without there being any logical (or even necessary) implication from ‘Today is Tuesday’ to ‘This is Belgium’. Relevance logicians are not themselves ...
Relevant and Substructural Logics
... premises to a conclusion, but rather relate lists, or other forms of structured collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define ...
... premises to a conclusion, but rather relate lists, or other forms of structured collections as premises, to a conclusion. This is because lists or other structures can distinguish the order or quantity of individual premises, while sets cannot. However, this is all that can simply be done to define ...
Combinaison des logiques temporelle et déontique pour la
... stay very pleasant. I learnt a lot about deontic logics and action logics. The collaboration that followed was really stimulating until the end of my PhD, and the logic proposed in this dissertation is its fruit. My acknowledgment then goes to Philippe Balbiani, for all the discussions we had, about ...
... stay very pleasant. I learnt a lot about deontic logics and action logics. The collaboration that followed was really stimulating until the end of my PhD, and the logic proposed in this dissertation is its fruit. My acknowledgment then goes to Philippe Balbiani, for all the discussions we had, about ...
Modal Languages and Bounded Fragments of Predicate Logic
... expressive modal formalisms (Venema 1991, De Rijke 1993). Of course, one can also study the effects of special frame restrictions – but we must leave this issue for further investigation, except for some passing remarks. What precisely are fragments of classical first-order logic showing “modal” beh ...
... expressive modal formalisms (Venema 1991, De Rijke 1993). Of course, one can also study the effects of special frame restrictions – but we must leave this issue for further investigation, except for some passing remarks. What precisely are fragments of classical first-order logic showing “modal” beh ...
Logic Part II: Intuitionistic Logic and Natural Deduction
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
... in many elds of mathematics, there are contradictory propositions from which anything is derivable ...
Many-Valued Logic
... none of the Lewis modal logics S1-S5 have finite characteristic matrices—meaning, among other things, that they cannot be viewed as many-valued systems with a finite number of truth values. ...
... none of the Lewis modal logics S1-S5 have finite characteristic matrices—meaning, among other things, that they cannot be viewed as many-valued systems with a finite number of truth values. ...
On modal logics of group belief
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
The Herbrand Manifesto
... In much of the literature, Herbrand semantics is treated (somewhat understandably) as a special case of Tarskian semantics - the case where we look at so-called Herbrand interpretations. Although the two are similar in many ways, they are not the same. First of all, in Tarskian semantics, there are ...
... In much of the literature, Herbrand semantics is treated (somewhat understandably) as a special case of Tarskian semantics - the case where we look at so-called Herbrand interpretations. Although the two are similar in many ways, they are not the same. First of all, in Tarskian semantics, there are ...
LINEAR LOGIC AS A FRAMEWORK FOR SPECIFYING SEQUENT
... where ∆ is the multiset union of ∆1 and ∆2 , and A is the multiset union of A1 and A2 . In other words, those subgoals immediately to the left of an ⇒ are attempted with empty bounded contexts: the bounded contexts, here ∆ and A, are divided up to be used to prove those goals immediately to the left ...
... where ∆ is the multiset union of ∆1 and ∆2 , and A is the multiset union of A1 and A2 . In other words, those subgoals immediately to the left of an ⇒ are attempted with empty bounded contexts: the bounded contexts, here ∆ and A, are divided up to be used to prove those goals immediately to the left ...
Essentials Of Symbolic Logic
... 2000 years. Both the Greek successors of Aristotle and the medieval scholastics made several important logical discoveries. But the importance of these discoveries was not realized at the time they were made. The general belief that all the important logical discoveries have been made by Aristotle n ...
... 2000 years. Both the Greek successors of Aristotle and the medieval scholastics made several important logical discoveries. But the importance of these discoveries was not realized at the time they were made. The general belief that all the important logical discoveries have been made by Aristotle n ...
Fichte`s Legacy in Logic
... Wissenschaftslehre should itself lead us to recognize a new logical form of judgment: the thetic judgment. Cataloging the various forms of judgment has long been a central part of logical theory. Just as the syllogistic figures specify the allowable forms of inference (the forms in accordance with w ...
... Wissenschaftslehre should itself lead us to recognize a new logical form of judgment: the thetic judgment. Cataloging the various forms of judgment has long been a central part of logical theory. Just as the syllogistic figures specify the allowable forms of inference (the forms in accordance with w ...
Intuitionistic and Modal Logic
... that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more than logic, since mathematics can be reduced to it, a view supported by Russell (not a Platonist) at th ...
... that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more than logic, since mathematics can be reduced to it, a view supported by Russell (not a Platonist) at th ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... will be a theory, because under the AGM setting only theories can be KBs. The inclusion postulate guarantees that the operation of contraction will not add any knowledge previously unknown to the KB; this would be irrational, as the contraction operation is used to remove knowledge from a KB. The po ...
... will be a theory, because under the AGM setting only theories can be KBs. The inclusion postulate guarantees that the operation of contraction will not add any knowledge previously unknown to the KB; this would be irrational, as the contraction operation is used to remove knowledge from a KB. The po ...
higher-order logic - University of Amsterdam
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
X - UOW
... 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 are reliable (“safe”) and are highly recommended if the “quick” method is confusing or leading nowhere! The quick met ...
... 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 are reliable (“safe”) and are highly recommended if the “quick” method is confusing or leading nowhere! The quick met ...