Proofs in Propositional Logic
... doesn’t change, or this application generates a finite sequence (possibly empty) of new subgoals, which replaces the previous one. ...
... doesn’t change, or this application generates a finite sequence (possibly empty) of new subgoals, which replaces the previous one. ...
Proofs in Propositional Logic
... doesn’t change, or this application generates a finite sequence (possibly empty) of new subgoals, which replaces the previous one. ...
... doesn’t change, or this application generates a finite sequence (possibly empty) of new subgoals, which replaces the previous one. ...
Introduction to Linear Logic
... University of Aarhus. All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ...
... University of Aarhus. All rights reserved. Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. ...
Introduction to Discrete Structures Introduction
... • Definition: Let A and B be two sets. The Cartesian product of A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a ...
... • Definition: Let A and B be two sets. The Cartesian product of A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a ...
ICS 353: Design and Analysis of Algorithms
... • The quantifiers and have higher precedence than all logical operators from propositional calculus. • E.g., x P(x) Q(x) • means……………………….. • does not mean …………………… ...
... • The quantifiers and have higher precedence than all logical operators from propositional calculus. • E.g., x P(x) Q(x) • means……………………….. • does not mean …………………… ...
Strong Logics of First and Second Order
... case along the second dimension, the formula Φ(x, y) singles out the powerset of M and many have thought that the mathematical entanglement1 with the powerset relation is too significant to warrant classifying the “logic”—full second-order logic—as a genuine logic. The question motivating this work ...
... case along the second dimension, the formula Φ(x, y) singles out the powerset of M and many have thought that the mathematical entanglement1 with the powerset relation is too significant to warrant classifying the “logic”—full second-order logic—as a genuine logic. The question motivating this work ...
The Emergence of First
... a logician used first-order logic and where, as more frequently occurred, he employed some richer form of logic. I have distinguished between a logician's use of first-order logic (where quantifiers range only over individuals), second-order logic (where quantifiers can also range over sets or relat ...
... a logician used first-order logic and where, as more frequently occurred, he employed some richer form of logic. I have distinguished between a logician's use of first-order logic (where quantifiers range only over individuals), second-order logic (where quantifiers can also range over sets or relat ...
Bilattices and the Semantics of Logic Programming
... two and the three valued semantical theories follow easily from work on Belnap’s four-valued version (because two and three valued logics are natural sublogics of the four-valued logic). And this is not unique to the four-valued case; with no more work similar results can be established for bilattic ...
... two and the three valued semantical theories follow easily from work on Belnap’s four-valued version (because two and three valued logics are natural sublogics of the four-valued logic). And this is not unique to the four-valued case; with no more work similar results can be established for bilattic ...
Acts of Commanding and Changing Obligations
... to open the window. In order to characterize effects of illocutionary acts adequately, we need to be able to isolate them from perlocutionary consequences of utterances. It is interesting to note, in this connection, that some illocutionary acts such as commanding, forbidding, permitting, and promis ...
... to open the window. In order to characterize effects of illocutionary acts adequately, we need to be able to isolate them from perlocutionary consequences of utterances. It is interesting to note, in this connection, that some illocutionary acts such as commanding, forbidding, permitting, and promis ...
Let me begin by reminding you of a number of passages ranging
... Nevertheless, I think it would be a serious mistake to dismiss these important remarks. First of all, as Frege proceeds to say a bit further on in the “My Basic Logical Insights” manuscript, it is precisely due to the logical imperfection of ordinary language that we seem to find ourselves obliged t ...
... Nevertheless, I think it would be a serious mistake to dismiss these important remarks. First of all, as Frege proceeds to say a bit further on in the “My Basic Logical Insights” manuscript, it is precisely due to the logical imperfection of ordinary language that we seem to find ourselves obliged t ...
propositional logic extended with a pedagogically useful relevant
... kinds. This is by no means necessary. One may study ways to remove one of the kinds of paradoxes. Some such ways may have effects on other paradoxes, but not all of them. The logic PCR was devised with the aim of removing only the paradoxes from (iii). In [3], paraconsistency is presented as a means ...
... kinds. This is by no means necessary. One may study ways to remove one of the kinds of paradoxes. Some such ways may have effects on other paradoxes, but not all of them. The logic PCR was devised with the aim of removing only the paradoxes from (iii). In [3], paraconsistency is presented as a means ...
A pragmatic dialogic interpretation of bi
... 1 Introduction. A mathematical prelude. The mathematical case study of this paper is a variant of Cecylia Rauzer’s bi-intuitionistic logic [48, 49] (called Heyting-Brouwer logic by Rauszer) and the relations between the two parts that can be identified within it, namely intuitionistic logic, on one ...
... 1 Introduction. A mathematical prelude. The mathematical case study of this paper is a variant of Cecylia Rauzer’s bi-intuitionistic logic [48, 49] (called Heyting-Brouwer logic by Rauszer) and the relations between the two parts that can be identified within it, namely intuitionistic logic, on one ...
On Decidability of Intuitionistic Modal Logics
... of first order logic. Unfortunately, the decidability proof does not give a good decision procedure since it proceeds by reduction to satisfiability of formulas of SkS (monadic second-order theory of trees with constant branching factor k, [11]) where decision procedure has non-elementary complexity ...
... of first order logic. Unfortunately, the decidability proof does not give a good decision procedure since it proceeds by reduction to satisfiability of formulas of SkS (monadic second-order theory of trees with constant branching factor k, [11]) where decision procedure has non-elementary complexity ...
Knowledge Representation and Reasoning
... Reasoning Morgan Kaufmann 2004 Poole D and Mackworth A Artificial intelligence : foundations of ...
... Reasoning Morgan Kaufmann 2004 Poole D and Mackworth A Artificial intelligence : foundations of ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
A Mathematical Introduction to Modal Logic
... In semantics theory that many linguists work on, modal logic helps a lot. Political scientists and economists try to come up with fair division algorithms and welfare theories that have game theoretical motivation with an underlying modal logical intuition. Moreover, game theory uses modal models to ...
... In semantics theory that many linguists work on, modal logic helps a lot. Political scientists and economists try to come up with fair division algorithms and welfare theories that have game theoretical motivation with an underlying modal logical intuition. Moreover, game theory uses modal models to ...
Introduction to Modal Logic - CMU Math
... Theorem (S5 is complete) If every model M with its accessibility relation an equivalence relation models ϕ then we can prove ϕ using the axioms S5, ie. this system is complete. ...
... Theorem (S5 is complete) If every model M with its accessibility relation an equivalence relation models ϕ then we can prove ϕ using the axioms S5, ie. this system is complete. ...
Partial Grounded Fixpoints
... sometimes, these generalisations even fill holes in their theory. E.g., while Bogaerts et al. [2015] showed that exact Astable fixpoints are grounded, we show that all A-stable fixpoints are A-grounded. Also, while Bogaerts et al. [2015] showed that, if the well-founded fixpoint is exact, then it is ...
... sometimes, these generalisations even fill holes in their theory. E.g., while Bogaerts et al. [2015] showed that exact Astable fixpoints are grounded, we show that all A-stable fixpoints are A-grounded. Also, while Bogaerts et al. [2015] showed that, if the well-founded fixpoint is exact, then it is ...
Paper - Department of Computer Science and Information Systems
... and admissible rules problems there does not even exist a recursive reduction of K4 with the universal modality to K4. Note that, on the other hand, for ‘reflexive’ modal logics with the universal modality such as S4, T or Grz the unification problem is trivially decidable (see the end of Section 2) ...
... and admissible rules problems there does not even exist a recursive reduction of K4 with the universal modality to K4. Note that, on the other hand, for ‘reflexive’ modal logics with the universal modality such as S4, T or Grz the unification problem is trivially decidable (see the end of Section 2) ...
Linear Contextual Modal Type Theory
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
... The central idea in linear logic [Gir87] is that of a resource. Linear assumptions play the role of a fixed set of available resources that must be consumed (exactly once) in a derivation. Therefore, available resources form the philosophical foundation of linear contextual modal logic. The idea of ...
Belief Revision in non
... However, the notion of consistency in the object logic may differ from that of classical logic. The AGM revision relies somehow on the notion of (classical) consistency. This can be easily understood by analysing postulate (K 3;4 ). Revision is only triggered when the new information is inconsisten ...
... However, the notion of consistency in the object logic may differ from that of classical logic. The AGM revision relies somehow on the notion of (classical) consistency. This can be easily understood by analysing postulate (K 3;4 ). Revision is only triggered when the new information is inconsisten ...
relevant reasoning as the logical basis of
... Almost all the current knowledge-based systems are directly or indirectly based on classical mathematical logic which gives no guarantee that the conclusion of a reasoning is necessarily relevant to its premises, even if the reasoning is valid in the sense of the classical mathematical logic. It is ...
... Almost all the current knowledge-based systems are directly or indirectly based on classical mathematical logic which gives no guarantee that the conclusion of a reasoning is necessarily relevant to its premises, even if the reasoning is valid in the sense of the classical mathematical logic. It is ...
Proof theory for modal logic
... to establish decidability and consistency results through a combinatorial analysis of derivations. This analysis is made possible by the conversion, called normalization, of a derivation to a normal form that does not contain redundant parts and that satisfies the subformula property, a basic requi ...
... to establish decidability and consistency results through a combinatorial analysis of derivations. This analysis is made possible by the conversion, called normalization, of a derivation to a normal form that does not contain redundant parts and that satisfies the subformula property, a basic requi ...
Fine`s Theorem on First-Order Complete Modal Logics
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...