Correction to: On the Logical Philosophy of Assertive Graphs
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
This erratum is to correct in the paper of Daniele Chiffi and AhtiVeikko Pietarinen, On the Logical Philosophy of Assertive Graphs. Word Count:
Rank  Word  Count 
0  erratum  1 
Excerpts:
... this erratum is to correct in the paper of ...

1  correct  1 
Excerpts:
... this erratum is to correct in the paper of daniele chiffi and ...

2  daniele  1 
Excerpts:
...is to correct in the paper of daniele chiffi and ahtiveikko pietarinen on the logical ...

3  chiffi  1 
Excerpts:
...to correct in the paper of daniele chiffi and ahtiveikko pietarinen on the logical philosophy ...

4  ahtiveikko  1 
Excerpts:
...in the paper of daniele chiffi and ahtiveikko pietarinen on the logical philosophy of assertive ...

5  pietarinen  1 
Excerpts:
...the paper of daniele chiffi and ahtiveikko pietarinen on the logical philosophy of assertive graphs ...

6  logical  1 
Excerpts:
...daniele chiffi and ahtiveikko pietarinen on the logical philosophy of assertive graphs ...

7  philosophy  1 
Excerpts:
...chiffi and ahtiveikko pietarinen on the logical philosophy of assertive graphs ...

8  assertive  1 
Excerpts:
...ahtiveikko pietarinen on the logical philosophy of assertive graphs ...

9  graphs  1 
Excerpts:
...pietarinen on the logical philosophy of assertive graphs ...

Iterated Admissibility Through Forcing in Strategic Belief Models
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving
\(m+1\)
rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality (
\(R\infty AR\)
), might not be satisfied by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we analyze the problem in a different framework. We redefine the notion of type as well as the epistemic notion of assumption. These new definitions are sufficient for the characterization of iterated admissibility as the class of strategies that indeed satisfy
\(R\infty AR\)
. One of the key methodological innovations in our approach involves defining a new notion of generic types and employing these in conjunction with Cohen's technique of forcing. Word Count:
Rank  Word  Count 
0  rationality  4 
Excerpts:
...iterated admissibility embodies a minimal criterion of rationality in interactions the epistemic characterization of this ...
...that are obtained under a condition called rationality and m assumption of rationality in complete ...
...condition called rationality and m assumption of rationality in complete lexicographic type structures on the ...
...limit condition with an infinity assumption of rationality
rinfty ...

1  iterated  3 
Excerpts:
... iterated admissibility embodies a minimal criterion of rationality ...
... rounds of iterated admissibility may be identified as those that ...
...definitions are sufficient for the characterization of iterated admissibility as the class of strategies that ...

2  types  3 
Excerpts:
...the epistemic structure if the class of types is complete and the types are continuous ...
...class of types is complete and the types are continuous in this paper we analyze ...
...involves defining a new notion of generic types and employing these in conjunction with cohens ...

3  notion  3 
Excerpts:
...in a different framework we redefine the notion of type as well as the epistemic ...
...of type as well as the epistemic notion of assumption these new definitions are sufficient ...
...in our approach involves defining a new notion of generic types and employing these in ...

4  assumption  3 
Excerpts:
...under a condition called rationality and m assumption of rationality in complete lexicographic type structures ...
...that its limit condition with an infinity assumption of rationality
...
...as well as the epistemic notion of assumption these new definitions are sufficient for the ...

5  epistemic  3 
Excerpts:
...minimal criterion of rationality in interactions the epistemic characterization of this solution has been actively ...
...be satisfied by any state in the epistemic structure if the class of types is ...
...notion of type as well as the epistemic notion of assumption these new definitions are ...

6  admissibility  3 
Excerpts:
... iterated admissibility embodies a minimal criterion of rationality in ...
... rounds of iterated admissibility may be identified as those that are ...
...are sufficient for the characterization of iterated admissibility as the class of strategies that indeed ...

7  been  3 
Excerpts:
...the epistemic characterization of this solution has been actively investigated in recent times it has ...
...actively investigated in recent times it has been shown that strategies surviving
...
...structures on the other hand it has been shown that its limit condition with an ...

8  type  2 
Excerpts:
...m assumption of rationality in complete lexicographic type structures on the other hand it has ...
...different framework we redefine the notion of type as well as the epistemic notion of ...

9  complete  2 
Excerpts:
...rationality and m assumption of rationality in complete lexicographic type structures on the other hand ...
...structure if the class of types is complete and the types are continuous in this ...

Natural Density and the Quantifier Most'
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form Most A are B', where A and B are plural nouns and the interpretations of A and B are infinite subsets of
\( \mathbb {N} \)
. There are two widely used semantics for Most A are B: (i)
\(C(A \cap B) > C(A\setminus B) \)
and (ii)
\( C(A\cap B) > \dfrac{C(A)}{2} \)
, where C(X) denotes the cardinality of a given finite set X. Although (i) is more descriptive than (ii), it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantityrelated statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of
\( \mathbb {N} \)
, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. Word Count:
Rank  Word  Count 
0  b  7 
Excerpts:
...sentences of the form most a are b where a and b are plural nouns ...
...most a are b where a and b are plural nouns and the interpretations of ...
...nouns and the interpretations of a and b are infinite subsets of
...
...widely used semantics for most a are b i
...
... ca cap b gt casetminus b
...
... ca cap b gt casetminus b
...
... cacap b gt dfracca2
...

1  infinite  4 
Excerpts:
...the interpretations of a and b are infinite subsets of
...
...alternative approach in deciding quantityrelated statements regarding infinite sets for this we introduce a new ...
...in which interpretations of their nouns are infinite subsets of
...
...it as applying to finite approximations of infinite sets computed to the limit ...

2  sentences  3 
Excerpts:
...proposes a formalization of the class of sentences quantified by most which is also interpreted ...
...on the domain of discourse we consider sentences of the form most a are b ...
...a new semantics using natural density for sentences in which interpretations of their nouns are ...

3  sets  3 
Excerpts:
...a considerable amount of insensitivity for certain sets since the quantifier most has a solid ...
...approach in deciding quantityrelated statements regarding infinite sets for this we introduce a new semantics ...
...as applying to finite approximations of infinite sets computed to the limit ...

4  semantics  3 
Excerpts:
... there are two widely used semantics for most a are b i
...
...sets for this we introduce a new semantics using natural density for sentences in which ...
...we take the standard definition of the semantics of most but define it as applying ...

5  under  2 
Excerpts:
...quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly ...
...and has a slightly more statistical behaviour under the interpretation proportional of we consider an ...

6  density  2 
Excerpts:
...we introduce a new semantics using natural density for sentences in which interpretations of their ...
...the axiomatization of the concept of natural density in other words we take the standard ...

7  ii  2 
Excerpts:
... and ii
...
...x although i is more descriptive than ii it also produces a considerable amount of ...

8  finite  2 
Excerpts:
...cx denotes the cardinality of a given finite set x although i is more descriptive ...
...most but define it as applying to finite approximations of infinite sets computed to the ...

9  gt  2 
Excerpts:
... ca cap b gt casetminus b
...
... cacap b gt dfracca2
...

On the Logical Philosophy of Assertive Graphs
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
The logic of assertive graphs (AGs) is a modification of Peirce's logic of existential graphs (EGs), which is intuitionistic and which takes assertions as its explicit object of study. In this paper we extend AGs into a classical graphical logic of assertions (ClAG) whose internal logic is classical. The characteristic feature is that both AGs and ClAG retain deepinference rules of transformation. Unlike classical EGs, both AGs and ClAG can do so without explicitly introducing polarities of areas in their language. We then compare advantages of these two graphical approaches to the logic of assertions with a reference to a number of topics in philosophy of logic and to their deepinferential nature of proofs. Word Count:
Rank  Word  Count 
0  logic  6 
Excerpts:
... the logic of assertive graphs ags is a modification ...
...graphs ags is a modification of peirces logic of existential graphs egs which is intuitionistic ...
...we extend ags into a classical graphical logic of assertions clag whose internal logic is ...
...graphical logic of assertions clag whose internal logic is classical the characteristic feature is that ...
...of these two graphical approaches to the logic of assertions with a reference to a ...
...a number of topics in philosophy of logic and to their deepinferential nature of proofs ...

1  ags  4 
Excerpts:
... the logic of assertive graphs ags is a modification of peirces logic of ...
...of study in this paper we extend ags into a classical graphical logic of assertions ...
...classical the characteristic feature is that both ags and clag retain deepinference rules of transformation ...
...rules of transformation unlike classical egs both ags and clag can do so without explicitly ...

2  assertions  3 
Excerpts:
...egs which is intuitionistic and which takes assertions as its explicit object of study in ...
...ags into a classical graphical logic of assertions clag whose internal logic is classical the ...
...two graphical approaches to the logic of assertions with a reference to a number of ...

3  clag  3 
Excerpts:
...into a classical graphical logic of assertions clag whose internal logic is classical the characteristic ...
...characteristic feature is that both ags and clag retain deepinference rules of transformation unlike classical ...
...transformation unlike classical egs both ags and clag can do so without explicitly introducing polarities ...

4  classical  3 
Excerpts:
...this paper we extend ags into a classical graphical logic of assertions clag whose internal ...
...of assertions clag whose internal logic is classical the characteristic feature is that both ags ...
...clag retain deepinference rules of transformation unlike classical egs both ags and clag can do ...

5  their  2 
Excerpts:
...without explicitly introducing polarities of areas in their language we then compare advantages of these ...
...topics in philosophy of logic and to their deepinferential nature of proofs ...

6  graphical  2 
Excerpts:
...paper we extend ags into a classical graphical logic of assertions clag whose internal logic ...
...we then compare advantages of these two graphical approaches to the logic of assertions with ...

7  both  2 
Excerpts:
...is classical the characteristic feature is that both ags and clag retain deepinference rules of ...
...deepinference rules of transformation unlike classical egs both ags and clag can do so without ...

8  egs  2 
Excerpts:
...modification of peirces logic of existential graphs egs which is intuitionistic and which takes assertions ...
...retain deepinference rules of transformation unlike classical egs both ags and clag can do so ...

9  graphs  2 
Excerpts:
... the logic of assertive graphs ags is a modification of peirces logic ...
...a modification of peirces logic of existential graphs egs which is intuitionistic and which takes ...

Towards an Algebraic Semantics for Implicatives
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
An algebraic semantics, based on factor algebras, for oneway and twoway implicative verbs is proposed. Implicative verbs denote elements of filters or of ideals generated by identity functions in factor algebras. This semantics explains in particular the problem of implicational equivalence raised by twoway implicative verbs, and shows that the negation necessary to establish the implicativity of these verbs is the negation which preserves the presuppositions of sentences with implicative verbs. In addition, it follows from the proposed semantics that any two implicative verbs denoting in the same algebra but belonging to different categories, are semantically related.
Word Count:
Rank  Word  Count 
0  verbs  6 
Excerpts:
...factor algebras for oneway and twoway implicative verbs is proposed implicative verbs denote elements of ...
...and twoway implicative verbs is proposed implicative verbs denote elements of filters or of ideals ...
...of implicational equivalence raised by twoway implicative verbs and shows that the negation necessary to ...
...necessary to establish the implicativity of these verbs is the negation which preserves the presuppositions ...
...preserves the presuppositions of sentences with implicative verbs in addition it follows from the proposed ...
...the proposed semantics that any two implicative verbs denoting in the same algebra but belonging ...

1  implicative  5 
Excerpts:
...on factor algebras for oneway and twoway implicative verbs is proposed implicative verbs denote elements ...
...oneway and twoway implicative verbs is proposed implicative verbs denote elements of filters or of ...
...problem of implicational equivalence raised by twoway implicative verbs and shows that the negation necessary ...
...which preserves the presuppositions of sentences with implicative verbs in addition it follows from the ...
...from the proposed semantics that any two implicative verbs denoting in the same algebra but ...

2  semantics  3 
Excerpts:
... an algebraic semantics based on factor algebras for oneway and ...
...by identity functions in factor algebras this semantics explains in particular the problem of implicational ...
...in addition it follows from the proposed semantics that any two implicative verbs denoting in ...

3  factor  2 
Excerpts:
... an algebraic semantics based on factor algebras for oneway and twoway implicative verbs ...
...of ideals generated by identity functions in factor algebras this semantics explains in particular the ...

4  algebras  2 
Excerpts:
... an algebraic semantics based on factor algebras for oneway and twoway implicative verbs is ...
...ideals generated by identity functions in factor algebras this semantics explains in particular the problem ...

5  twoway  2 
Excerpts:
...based on factor algebras for oneway and twoway implicative verbs is proposed implicative verbs denote ...
...the problem of implicational equivalence raised by twoway implicative verbs and shows that the negation ...

6  proposed  2 
Excerpts:
...for oneway and twoway implicative verbs is proposed implicative verbs denote elements of filters or ...
...verbs in addition it follows from the proposed semantics that any two implicative verbs denoting ...

7  negation  2 
Excerpts:
...twoway implicative verbs and shows that the negation necessary to establish the implicativity of these ...
...the implicativity of these verbs is the negation which preserves the presuppositions of sentences with ...

8  algebraic  1 
Excerpts:
... an algebraic semantics based on factor algebras for oneway ...

9  follows  1 
Excerpts:
...sentences with implicative verbs in addition it follows from the proposed semantics that any two ...

A FourValued Dynamic Epistemic Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a fourvalued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents' knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge'or more appropriately, belief'is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we present an intuition and possible application for manyvalued modal logics, and on the other hand we develop a logic that models the dynamics of evidence in a simple and intuitively clear fashion. Word Count:
Rank  Word  Count 
0  evidence  4 
Excerpts:
...only knowledge about the available information or evidence which can be incomplete or conflicting but ...
...facts this layer of available information or evidence which is the object of the agents ...
...knowledgeor more appropriately beliefis entirely based on evidence the technical results include a set of ...
...a logic that models the dynamics of evidence in a simple and intuitively clear fashion ...

1  epistemic  3 
Excerpts:
... epistemic logic is usually employed to model two ...
...of a situation the factual and the epistemic aspects truth however is not always attainable ...
...this paper we will explore a fourvalued epistemic logic designed to deal with these situations ...

2  logic  3 
Excerpts:
... epistemic logic is usually employed to model two aspects ...
...paper we will explore a fourvalued epistemic logic designed to deal with these situations where ...
...on the other hand we develop a logic that models the dynamics of evidence in ...

3  available  3 
Excerpts:
...to reason only with whatever information is available to us in this paper we will ...
...where agents have only knowledge about the available information or evidence which can be incomplete ...
...not explicitly about facts this layer of available information or evidence which is the object ...

4  information  3 
Excerpts:
...are forced to reason only with whatever information is available to us in this paper ...
...agents have only knowledge about the available information or evidence which can be incomplete or ...
...explicitly about facts this layer of available information or evidence which is the object of ...

5  only  2 
Excerpts:
...many cases we are forced to reason only with whatever information is available to us ...
...deal with these situations where agents have only knowledge about the available information or evidence ...

6  knowledge  2 
Excerpts:
...with these situations where agents have only knowledge about the available information or evidence which ...
...which is the object of the agents knowledge can be seen as a database by ...

7  agents  2 
Excerpts:
...designed to deal with these situations where agents have only knowledge about the available information ...
...evidence which is the object of the agents knowledge can be seen as a database ...

8  where  2 
Excerpts:
...logic designed to deal with these situations where agents have only knowledge about the available ...
...semantics we prepare the ground for logics where the notion of knowledgeor more appropriately beliefis ...

9  hand  2 
Excerpts:
...our contributions are twofold on the one hand we present an intuition and possible application ...
...manyvalued modal logics and on the other hand we develop a logic that models the ...

Formalizing GDPR Provisions in Reified I/O Logic: The DAPRECO Knowledge Base
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201201
Abstract:
The DAPRECO knowledge base is the main outcome of the interdisciplinary project bearing the same name (https://www.fnr.lu/projects/dataprotectionregulationcompliance). It is a repository of rules written in LegalRuleML, an XML formalism designed to be a standard for representing the semantic and logical content of legal documents. The rules represent the provisions of the General Data Protection Regulation (GDPR), the new Regulation that is significantly affecting the digital market in the European Union and beyond. The DAPRECO knowledge base builds upon the Privacy Ontology (PrOnto) (Palmirani et al in Proceedings of the 7th international conference on electronic government and the information systems perspective: technologyenabled innovation for democracy, government and governance, 2018c), which provides a model for the legal concepts involved in the GDPR, by adding a further layer of constraints in the form of ifthen rules, referring either to standard first order logic implications or to deontic statements. Ifthen rules are formalized in reified Input/Output logic (Robaldo and Sun in J Log Comput 7, 2017) and then codified in LegalRuleML. Reified Input/Output logic is an application of standard Input/Output logic for legal reasoning, in which Input/Output logic is combined with the reificationbased approach in Hobbs and Gordon (A formal theory of commonsense psychology, how people think people think. Cambridge University Press, Cambridge, 2017). The DAPRECO knowledge base is then a case study for reified Input/Output logic, and it shows that the formalism indeed appears to be a good candidate to effectively formalize, via uniform and simple (flat) representations, complex linguistic/deontic phenomena that may be found in legal texts. To date, the DAPRECO knowledge base is the biggest knowledge base in LegalRuleML and Input/Output logic freely available online (https://github.com/dapreco/daprecokb/blob/master/gdpr/rioKB_GDPR.xml). Word Count:
Rank  Word  Count 
0  logic  7 
Excerpts:
...rules referring either to standard first order logic implications or to deontic statements ifthen rules ...
...ifthen rules are formalized in reified inputoutput logic robaldo and sun in j log comput ...
...and then codified in legalruleml reified inputoutput logic is an application of standard inputoutput logic ...
...logic is an application of standard inputoutput logic for legal reasoning in which inputoutput logic ...
...logic for legal reasoning in which inputoutput logic is combined with the reificationbased approach in ...
...then a case study for reified inputoutput logic and it shows that the formalism indeed ...
...biggest knowledge base in legalruleml and inputoutput logic freely available online httpsgithubcomdaprecodaprecokbblobmastergdprriokbgdprxml ...

1  inputoutput  6 
Excerpts:
...statements ifthen rules are formalized in reified inputoutput logic robaldo and sun in j log ...
...2017 and then codified in legalruleml reified inputoutput logic is an application of standard inputoutput ...
...inputoutput logic is an application of standard inputoutput logic for legal reasoning in which inputoutput ...
...inputoutput logic for legal reasoning in which inputoutput logic is combined with the reificationbased approach ...
...is then a case study for reified inputoutput logic and it shows that the formalism ...
...the biggest knowledge base in legalruleml and inputoutput logic freely available online httpsgithubcomdaprecodaprecokbblobmastergdprriokbgdprxml ...

2  knowledge  5 
Excerpts:
... the dapreco knowledge base is the main outcome of the ...
...the european union and beyond the dapreco knowledge base builds upon the privacy ontology pronto ...
...cambridge university press cambridge 2017 the dapreco knowledge base is then a case study for ...
...in legal texts to date the dapreco knowledge base is the biggest knowledge base in ...
...the dapreco knowledge base is the biggest knowledge base in legalruleml and inputoutput logic freely ...

3  base  5 
Excerpts:
... the dapreco knowledge base is the main outcome of the interdisciplinary ...
...european union and beyond the dapreco knowledge base builds upon the privacy ontology pronto palmirani ...
...university press cambridge 2017 the dapreco knowledge base is then a case study for reified ...
...legal texts to date the dapreco knowledge base is the biggest knowledge base in legalruleml ...
...dapreco knowledge base is the biggest knowledge base in legalruleml and inputoutput logic freely available ...

4  dapreco  4 
Excerpts:
... the dapreco knowledge base is the main outcome of ...
...in the european union and beyond the dapreco knowledge base builds upon the privacy ontology ...
...think cambridge university press cambridge 2017 the dapreco knowledge base is then a case study ...
...found in legal texts to date the dapreco knowledge base is the biggest knowledge base ...

5  legal  4 
Excerpts:
...representing the semantic and logical content of legal documents the rules represent the provisions of ...
...2018c which provides a model for the legal concepts involved in the gdpr by adding ...
...an application of standard inputoutput logic for legal reasoning in which inputoutput logic is combined ...
...linguisticdeontic phenomena that may be found in legal texts to date the dapreco knowledge base ...

6  rules  4 
Excerpts:
...name httpswwwfnrluprojectsdataprotectionregulationcompliance it is a repository of rules written in legalruleml an xml formalism designed ...
...and logical content of legal documents the rules represent the provisions of the general data ...
...of constraints in the form of ifthen rules referring either to standard first order logic ...
...logic implications or to deontic statements ifthen rules are formalized in reified inputoutput logic robaldo ...

7  standard  3 
Excerpts:
...an xml formalism designed to be a standard for representing the semantic and logical content ...
...form of ifthen rules referring either to standard first order logic implications or to deontic ...
...reified inputoutput logic is an application of standard inputoutput logic for legal reasoning in which ...

8  reified  3 
Excerpts:
...deontic statements ifthen rules are formalized in reified inputoutput logic robaldo and sun in j ...
...7 2017 and then codified in legalruleml reified inputoutput logic is an application of standard ...
...base is then a case study for reified inputoutput logic and it shows that the ...

9  legalruleml  3 
Excerpts:
...is a repository of rules written in legalruleml an xml formalism designed to be a ...
...comput 7 2017 and then codified in legalruleml reified inputoutput logic is an application of ...
...base is the biggest knowledge base in legalruleml and inputoutput logic freely available online httpsgithubcomdaprecodaprecokbblobmastergdprriokbgdprxml ...

A Basic Dual Intuitionistic Logic and Some of its Extensions Included in G3 $$_{\text {DH}}$$
DH
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201101
Abstract:
The logic DHb is the result of extending Sylvan and Plumwood's minimal De Morgan logic B
\(_{\text {M}}\)
with a dual intuitionistic negation of the type Sylvan defined for the extension CC
\(\omega \)
of da Costa's paraconsistent logic C
\(\omega \)
. We provide Routley“Meyer ternary relational semantics with a set of designated points for DHb and a wealth of its extensions included in G3
\(_{\text {DH}}\)
, the expansion of G3
\(_{+}\)
with a dual intuitionistic negation of the kind considered by Sylvan (G3
\(_{+}\)
is the positive fragment of GÃ¶delian 3valued logic G3). All logics in the paper are paraconsistent. Word Count:
The MultiplicativeAdditive Lambek Calculus with Subexponential and Bracket Modalities
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201021
Abstract:
We give a prooftheoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill's calculi, and focus on their fragments including multiplicative (Lambek) connectives, additive conjunction and disjunction, brackets and bracket modalities, and the ! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut (cut elimination theorem). We also prove algorithmic undecidability for both calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages. Word Count:
Rank  Word  Count 
0  cut  3 
Excerpts:
...systems we resolve issues connected with the cut rule and provide necessary modifications after which ...
...modifications after which we prove admissibility of cut cut elimination theorem we also prove algorithmic ...
...after which we prove admissibility of cut cut elimination theorem we also prove algorithmic undecidability ...

1  prove  2 
Excerpts:
...and provide necessary modifications after which we prove admissibility of cut cut elimination theorem we ...
...of cut cut elimination theorem we also prove algorithmic undecidability for both calculi and show ...

2  algorithmic  2 
Excerpts:
... we give a prooftheoretic and algorithmic complexity analysis for systems introduced by morrill ...
...cut cut elimination theorem we also prove algorithmic undecidability for both calculi and show that ...

3  both  2 
Excerpts:
...modalities and the subexponential modality for both systems we resolve issues connected with the ...
...theorem we also prove algorithmic undecidability for both calculi and show that categorial grammars based ...

4  systems  2 
Excerpts:
...a prooftheoretic and algorithmic complexity analysis for systems introduced by morrill to serve as the ...
...and the subexponential modality for both systems we resolve issues connected with the cut ...

5  categorial  2 
Excerpts:
...serve as the core of the catlog categorial grammar parser we consider two recent versions ...
...undecidability for both calculi and show that categorial grammars based on them can generate arbitrary ...

6  calculi  2 
Excerpts:
...we consider two recent versions of morrills calculi and focus on their fragments including multiplicative ...
...we also prove algorithmic undecidability for both calculi and show that categorial grammars based on ...

7  give  1 
Excerpts:
... we give a prooftheoretic and algorithmic complexity analysis for ...

8  resolve  1 
Excerpts:
... subexponential modality for both systems we resolve issues connected with the cut rule and ...

9  issues  1 
Excerpts:
...subexponential modality for both systems we resolve issues connected with the cut rule and provide ...

LefttoRight Asymmetry and Early Association in Korean
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20201007
Abstract:
This paper shows Korean speakers' strong preference for incremental structure building based on the following core phenomena: (1) left“right asymmetry; (2) preverbal structure building and a strong preference for early association. This paper argues that these phenomena reflect the procedural aspects of linguistic competence, which are difficult to explain within nonprocedural grammar formalisms. Based on these observations, I argue for the necessity of a grammar formalism that adopts lefttoright incrementality as a core property of the syntactic architecture. In particular, I aim to show the role of (1) constructive particles; (2) prosody; and (3) structural routines in incremental Korean structure building. Though the nature of this discussion is theoryneutral, in order to formalise this idea I will adopt Dynamic Syntax [DS: Kempson et al. (Dynamic syntax: the flow of language understanding, Blackwell, Oxford, 2001); Cann et al. (The dynamics of language. Elsevier, Oxford, 2005)] in this paper. Word Count:
A History Based Logic for Dynamic Preference Updates
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200901
Abstract:
History based models suggest a processbased approach to epistemic and temporal reasoning. In this work, we introduce preferences to history based models. Motivated by game theoretical observations, we discuss how preferences can dynamically be updated in history based models. Following, we consider arrow update logic and event calculus, and give history based models for these logics. This allows us to relate dynamic logics of history based models to a broader framework. Word Count:
Rank  Word  Count 
0  history  5 
Excerpts:
... history based models suggest a processbased approach to ...
...in this work we introduce preferences to history based models motivated by game theoretical observations ...
...how preferences can dynamically be updated in history based models following we consider arrow update ...
...update logic and event calculus and give history based models for these logics this allows ...
...allows us to relate dynamic logics of history based models to a broader framework ...

1  based  5 
Excerpts:
... history based models suggest a processbased approach to epistemic ...
...this work we introduce preferences to history based models motivated by game theoretical observations we ...
...preferences can dynamically be updated in history based models following we consider arrow update logic ...
...logic and event calculus and give history based models for these logics this allows us ...
...us to relate dynamic logics of history based models to a broader framework ...

2  models  5 
Excerpts:
... history based models suggest a processbased approach to epistemic and ...
...work we introduce preferences to history based models motivated by game theoretical observations we discuss ...
...can dynamically be updated in history based models following we consider arrow update logic and ...
...and event calculus and give history based models for these logics this allows us to ...
...to relate dynamic logics of history based models to a broader framework ...

3  logics  2 
Excerpts:
...and give history based models for these logics this allows us to relate dynamic logics ...
...logics this allows us to relate dynamic logics of history based models to a broader ...

4  preferences  2 
Excerpts:
...temporal reasoning in this work we introduce preferences to history based models motivated by game ...
...by game theoretical observations we discuss how preferences can dynamically be updated in history based ...

5  broader  1 
Excerpts:
...logics of history based models to a broader framework ...

6  dynamic  1 
Excerpts:
...these logics this allows us to relate dynamic logics of history based models to a ...

7  relate  1 
Excerpts:
...for these logics this allows us to relate dynamic logics of history based models to ...

8  allows  1 
Excerpts:
...history based models for these logics this allows us to relate dynamic logics of history ...

9  following  1 
Excerpts:
...dynamically be updated in history based models following we consider arrow update logic and event ...

A Note on the Issue of Cohesiveness in Canonical Models
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200901
Abstract:
In their presentation of canonical models for normal systems of modal logic, Hughes and Cresswell observe that some of these models are based on a frame which can be also thought of as a collection of two or more isolated frames; they call such frames ˜noncohesive'. The problem of checking whether the canonical model of a given system is cohesive is still rather unexplored and no general decision procedure is available. The main contribution of this article consists in introducing a method which is sufficient to show that canonical models of some relevant classes of normal monomodal and bimodal systems are always noncohesive.
Word Count:
The Class of All Natural Implicative Expansions of Kleene's Strong Logic Functionally Equivalent to Åkasiewicz's 3Valued Logic Å3
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200901
Abstract:
We consider the logics determined by the set of all natural implicative expansions of Kleene's strong 3valued matrix (with both only one and two designated values) and select the class of all logics functionally equivalent to Åukasiewicz's 3valued logic Å3. The concept of a natural implicative matrix' is based upon the notion of a natural conditional' defined in Tomova (Rep Math Log 47:173“182, 2012). Word Count:
The Thin Red Line, Molinism, and the Flow of Time
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200901
Abstract:
In addressing the problem of the (in)compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line (
\(\mathsf {TRL}\)
) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism and
\(\mathsf {TRL}\)
models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227“239, 2011) has advanced some criticisms of Molinism that have also been leveled against
\(\mathsf {TRL}\)
models. In particular, Restall believes that the implication
\(p \rightarrow \mathbf {HF}p\)
is not true in
\(\mathsf {TRL}\)
models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall's criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models (not just
\(\mathsf {TRL}\)
) the implication
\(p \rightarrow \mathbf {HF}p\)
is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the
\(\mathsf {TRL}\)
and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either. Word Count:
Underspecification, Parsing Mismatches and Routinisation: The Historical Development of the Clitic Systems of Greek Dialects
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200820
Abstract:
In this paper, the historical development of the clitic systems of Standard Modern, Cypriot and Pontic Greek is discussed. These three varieties not only present the whole range of variation one can find across clitic systems in Greek but, furthermore, derive from a common linguistic ancestor, i.e. Koine Greek. This paper argues that the transition from Koine Greek to the Medieval varieties and from the Medieval varieties to the respective modern ones can be explained by making the assumption that routinisation (in the sense of Pickering and Garrod in Behav Brain Sci 27:169“226, 2004) and parsing/hearer assymetries are two important factors behind syntactic change. The claim is that the transition from Koine to the Medieval Greek varieties involves the emergence of a clitic system with encoded syntactic constraints out of a freer one, where clitic positioning was regulated by pragmatic preferences rather than syntactic constraints. Then, the transition to the modern varieties from the respective medieval ones is explained, at least partly, on the assumption that production/parsing mismatches are capable of triggering syntactic change. This last assumption combined with: (a) the tendency to obtain more generalised parsing triggers for parsing the individual clitics and (b) the fact that the Medieval varieties in question differ in minimal but crucial ways, provides us an explanation for the transition to the modern varieties. Word Count:
On Relation Between Linear Temporal Logic and Quantum Finite Automata
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
Linear temporal logic is a widely used method for verification of model checking and expressing the system specifications. The relationship between theory of automata and logic had a great influence in the computer science. Investigation of the relationship between quantum finite automata and linear temporal logic is a natural goal. In this paper, we present a construction of quantum finite automata on finite words from lineartime temporal logic formulas. Further, the relation between quantum finite automata and linear temporal logic is explored in terms of language recognition and acceptance probability. We have shown that the class of languages accepted by quantum finite automata are definable in linear temporal logic, except for measureonce oneway quantum finite automata. Word Count:
Rank  Word  Count 
0  finite  6 
Excerpts:
...science investigation of the relationship between quantum finite automata and linear temporal logic is a ...
...paper we present a construction of quantum finite automata on finite words from lineartime temporal ...
...a construction of quantum finite automata on finite words from lineartime temporal logic formulas further ...
...logic formulas further the relation between quantum finite automata and linear temporal logic is explored ...
...the class of languages accepted by quantum finite automata are definable in linear temporal logic ...
...temporal logic except for measureonce oneway quantum finite automata ...

1  automata  6 
Excerpts:
...system specifications the relationship between theory of automata and logic had a great influence in ...
...investigation of the relationship between quantum finite automata and linear temporal logic is a natural ...
...we present a construction of quantum finite automata on finite words from lineartime temporal logic ...
...formulas further the relation between quantum finite automata and linear temporal logic is explored in ...
...class of languages accepted by quantum finite automata are definable in linear temporal logic except ...
...logic except for measureonce oneway quantum finite automata ...

2  logic  6 
Excerpts:
... linear temporal logic is a widely used method for verification ...
...the relationship between theory of automata and logic had a great influence in the computer ...
...between quantum finite automata and linear temporal logic is a natural goal in this paper ...
...automata on finite words from lineartime temporal logic formulas further the relation between quantum finite ...
...between quantum finite automata and linear temporal logic is explored in terms of language recognition ...
...finite automata are definable in linear temporal logic except for measureonce oneway quantum finite automata ...

3  temporal  5 
Excerpts:
... linear temporal logic is a widely used method for ...
...relationship between quantum finite automata and linear temporal logic is a natural goal in this ...
...finite automata on finite words from lineartime temporal logic formulas further the relation between quantum ...
...relation between quantum finite automata and linear temporal logic is explored in terms of language ...
...quantum finite automata are definable in linear temporal logic except for measureonce oneway quantum finite ...

4  quantum  5 
Excerpts:
...computer science investigation of the relationship between quantum finite automata and linear temporal logic is ...
...this paper we present a construction of quantum finite automata on finite words from lineartime ...
...temporal logic formulas further the relation between quantum finite automata and linear temporal logic is ...
...that the class of languages accepted by quantum finite automata are definable in linear temporal ...
...linear temporal logic except for measureonce oneway quantum finite automata ...

5  linear  4 
Excerpts:
... linear temporal logic is a widely used method ...
...the relationship between quantum finite automata and linear temporal logic is a natural goal in ...
...the relation between quantum finite automata and linear temporal logic is explored in terms of ...
...by quantum finite automata are definable in linear temporal logic except for measureonce oneway quantum ...

6  relationship  2 
Excerpts:
...checking and expressing the system specifications the relationship between theory of automata and logic had ...
...in the computer science investigation of the relationship between quantum finite automata and linear temporal ...

7  verification  1 
Excerpts:
...logic is a widely used method for verification of model checking and expressing the system ...

8  recognition  1 
Excerpts:
...logic is explored in terms of language recognition and acceptance probability we have shown that ...

9  formulas  1 
Excerpts:
...on finite words from lineartime temporal logic formulas further the relation between quantum finite automata ...

Formal Semantics and Applied Mathematics: An Inferential Account
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
In this paper, I utilise the growing literature on scientific modelling to investigate the nature of formal semantics from the perspective of the philosophy of science. Specifically, I incorporate the inferential framework proposed by Bueno and Colyvan (Nous 45(2): 345“374, 2011) in the philosophy of applied mathematics to offer an account of how formal semantics explains and models its data. This view produces a picture of formal semantic models as involving an embedded process of inference and representation applying indirectly to linguistic phenomena. The final aim of the paper is directed at proposing a novel account of the syntax“semantics interface while shedding light on empty categories, semantically null forms, underspecified content and compositionality as a whole. Word Count:
Residual Contraction
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
In this paper, we propose and axiomatically characterize residual contractions, a new kind of contraction operators for belief bases. We establish that the class of partial meet contractions is a strict subclass of the class of residual contractions. We identify an extra condition that may be added to the definition of residual contractions, which is such that the class of residual contractions that satisfy it coincides with the class of partial meet contractions. We investigate the interrelations in the sense of (strict) inclusion among the class of residual contractions and other classes of well known contraction operators for belief bases. Word Count:
Rank  Word  Count 
0  contractions  7 
Excerpts:
...paper we propose and axiomatically characterize residual contractions a new kind of contraction operators for ...
...establish that the class of partial meet contractions is a strict subclass of the class ...
...strict subclass of the class of residual contractions we identify an extra condition that may ...
...be added to the definition of residual contractions which is such that the class of ...
...is such that the class of residual contractions that satisfy it coincides with the class ...
...coincides with the class of partial meet contractions we investigate the interrelations in the sense ...
...strict inclusion among the class of residual contractions and other classes of well known contraction ...

1  residual  5 
Excerpts:
...this paper we propose and axiomatically characterize residual contractions a new kind of contraction operators ...
...a strict subclass of the class of residual contractions we identify an extra condition that ...
...may be added to the definition of residual contractions which is such that the class ...
...which is such that the class of residual contractions that satisfy it coincides with the ...
...of strict inclusion among the class of residual contractions and other classes of well known ...

2  bases  2 
Excerpts:
...new kind of contraction operators for belief bases we establish that the class of partial ...
...of well known contraction operators for belief bases ...

3  meet  2 
Excerpts:
...we establish that the class of partial meet contractions is a strict subclass of the ...
...it coincides with the class of partial meet contractions we investigate the interrelations in the ...

4  contraction  2 
Excerpts:
...characterize residual contractions a new kind of contraction operators for belief bases we establish that ...
...contractions and other classes of well known contraction operators for belief bases ...

5  operators  2 
Excerpts:
...residual contractions a new kind of contraction operators for belief bases we establish that the ...
...and other classes of well known contraction operators for belief bases ...

6  belief  2 
Excerpts:
...a new kind of contraction operators for belief bases we establish that the class of ...
...classes of well known contraction operators for belief bases ...

7  strict  2 
Excerpts:
...class of partial meet contractions is a strict subclass of the class of residual contractions ...
...investigate the interrelations in the sense of strict inclusion among the class of residual contractions ...

8  partial  2 
Excerpts:
...bases we establish that the class of partial meet contractions is a strict subclass of ...
...satisfy it coincides with the class of partial meet contractions we investigate the interrelations in ...

9  investigate  1 
Excerpts:
...the class of partial meet contractions we investigate the interrelations in the sense of strict ...

Confused Terms in Ordinary Language
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
Confused terms appear to signify more than one entity. Carnap (Meaning and necessity, University of Chicago Press, Chicago, 1956) maintained that any putative name that is associated with more than one object in a relevant universe of discourse fails to be a genuine name. Although many philosophers have agreed with Carnap, they have not always agreed among themselves about the truthvalues of atomic sentences containing such terms. Some hold that such atomic sentences are always false, and others claim they are always truthvalueless. Field (J Philos 70:462“481, 1973) maintained that confused terms can still refer, albeit partially, and offered a supervaluational account of their semantic properties on which some atomic sentences with confused terms can be true. After outlining many of the most important theoretical considerations for and against various semantic theories for such terms, we report the results of a study designed to investigate which of these accounts best accords with the truthvalue judgments of ordinary language users about sentences containing these terms. We found that naÃ¯ve participants view confused names as capable of successfully referring to one or more objects. Thus, semantic theories that judge them to involve total reference failure do not comport well with patterns of ordinary usage. Word Count:
Truth Diagrams Versus Extant Notations for Propositional Logic
 Author: Error: Author not contained in standard '<author>' tag in feed
 Publication date: 20200601
Abstract:
Truth diagrams (TDs) are introduced as a novel graphical representation for propositional logic (PL). To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege's conceptual notation, diagrams from Wittgenstein's Tractatus, Pierce's alpha graphs and Gardner's shuttle diagrams. The comparison of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary. Word Count:
Rank  Word  Count 
0  pl  6 
Excerpts:
...a novel graphical representation for propositional logic pl to demonstrate their epistemic efficacy a set ...
...are proposed that any comprehensive representation for pl should encompass tds address all the criteria ...
...criteria whereas seven other existing representations for pl only provide partial coverage these existing representations ...
...the linear formula notation truth tables a pl specific interpretation of venn diagrams freges conceptual ...
...in distinguishing ideas that are fundamental to pl from features of common pl representations that ...
...fundamental to pl from features of common pl representations that are somewhat arbitrary ...

1  diagrams  4 
Excerpts:
... truth diagrams tds are introduced as a novel graphical ...
...tables a pl specific interpretation of venn diagrams freges conceptual notation diagrams from wittgensteins tractatus ...
...interpretation of venn diagrams freges conceptual notation diagrams from wittgensteins tractatus pierces alpha graphs and ...
...tractatus pierces alpha graphs and gardners shuttle diagrams the comparison of the representations succeeds in ...

2  representations  4 
Excerpts:
...all the criteria whereas seven other existing representations for pl only provide partial coverage these ...
...pl only provide partial coverage these existing representations are the linear formula notation truth tables ...
...gardners shuttle diagrams the comparison of the representations succeeds in distinguishing ideas that are fundamental ...
...to pl from features of common pl representations that are somewhat arbitrary ...

3  truth  2 
Excerpts:
... truth diagrams tds are introduced as a novel ...
...existing representations are the linear formula notation truth tables a pl specific interpretation of venn ...

4  tds  2 
Excerpts:
... truth diagrams tds are introduced as a novel graphical representation ...
...any comprehensive representation for pl should encompass tds address all the criteria whereas seven other ...

5  existing  2 
Excerpts:
...address all the criteria whereas seven other existing representations for pl only provide partial coverage ...
...for pl only provide partial coverage these existing representations are the linear formula notation truth ...

6  representation  2 
Excerpts:
...tds are introduced as a novel graphical representation for propositional logic pl to demonstrate their ...
...28 concepts are proposed that any comprehensive representation for pl should encompass tds address all ...

7  notation  2 
Excerpts:
...these existing representations are the linear formula notation truth tables a pl specific interpretation of ...
...specific interpretation of venn diagrams freges conceptual notation diagrams from wittgensteins tractatus pierces alpha graphs ...

8  tractatus  1 
Excerpts:
...diagrams freges conceptual notation diagrams from wittgensteins tractatus pierces alpha graphs and gardners shuttle diagrams ...

9  tables  1 
Excerpts:
...representations are the linear formula notation truth tables a pl specific interpretation of venn diagrams ...

