ABSTRACT In the present paper we analyse how intuitionist negation relates to the concept of triv... more ABSTRACT In the present paper we analyse how intuitionist negation relates to the concept of triviality. A proposition is trivial if it implies every other proposition. We claim that for natural deduction intuitionist logic such concept affords us a negation introduction rule schema that corresponds by the inversion principle to the usual negation elimination shcema, ex contradictionerm quodlibet .1
ABSTRACT In this paper we are going to examine intuitionistic sequent calculus and its negation r... more ABSTRACT In this paper we are going to examine intuitionistic sequent calculus and its negation rules. We state new negation rules defining, in this way, a new sequent system. It will be used to clarify Gentzen's NJ and LJ systems isomorphism. These new negation rules are a direct reading of new natural deduction negation rules obtained by a slight modification of NJ rules. We also show that the new system is equivalent to LJ and that the Hauptsatz holds for it.
This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to... more This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to be proposed is called Hypo. Concerning the meaning of logical constants, it adopts a conceptual point of view that diverges from “transmission” approaches of semantics – those based either on “truth transmission” or on “proof (construction) transmission”. We claim Hypo to be a constructive semantics. It does not require any principle going beyond what intuitionists would consider as acceptable for its statement. Its basic primitive relation is the relation of semantical consequence. Logical constants’ meaning is made explicit in terms of this relation. Clauses characterizing semantical consequence for logical constants establish sufficient and necessary conditions for the occurrence of a logical constant either as a hypothesis among others or as a consequence of a set of hypotheses. A hypothesis is a sentential content which is used pragmatically in an invitation - either we invite or we are invited to put under supposition this content. Semantically, it is taken as if it were true. An act of invitation is entirely distinct from the act of assertion or judgment. Hypo is modular. For each constant one clause explains its behavior. Hypotheses are explained via structural principles not involving logical constants. Also, Hypo can be extended to cover Classical Sentential Logic. Inferential validity for both cases, Intuitionist and Classical, is a derived concept.
This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to... more This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to be proposed is called Hypo. Concerning the meaning of logical constants, it adopts a conceptual point of view that diverges from "transmission" approaches of semantics-those based either on "truth transmission" or on "proof (construction) transmission". We claim Hypo to be a constructive semantics. It does not require any principle going beyond what intuitionists would consider as acceptable for its statement. Its basic primitive relation is the relation of semantical consequence semantical consequence semantical consequence semantical consequence. Logical constants' meaning is made explicit in terms of this relation. Clauses characterizing semantical consequence for logical constants establish sufficient and necessary conditions for the occurrence of a logical constant either as a hypothesi hypothesi hypothesi hypothesis s s s among others or as a consequence of a set of hypotheses. A hypothesis hypothesis hypothesis hypothesis is a sentential content which is used pragmatically in an invitation-either we invite or we are invited to put under supposition this content. Semantically, it is taken as if it were true. An act of invitation is entirely distinct from the act of assertion or judgment. Hypo is modular. For each constant one clause explains its behavior. Hypotheses are explained via structural principles not involving logical constants. Also, Hypo can be extended to cover Classical Sentential Logic. Inferential validity for both cases, Intuitionist and Classical, is a derived concept.
This is a constructivist semantical analysis of propositional constants in which the concept of h... more This is a constructivist semantical analysis of propositional constants in which the concept of hypothesis is taken as a primitive concept. The goal is to present a new semantics for propositional intuitionistic logic together with soundness and completeness.
ABSTRACT In the present paper we analyse how intuitionist negation relates to the concept of triv... more ABSTRACT In the present paper we analyse how intuitionist negation relates to the concept of triviality. A proposition is trivial if it implies every other proposition. We claim that for natural deduction intuitionist logic such concept affords us a negation introduction rule schema that corresponds by the inversion principle to the usual negation elimination shcema, ex contradictionerm quodlibet .1
ABSTRACT In this paper we are going to examine intuitionistic sequent calculus and its negation r... more ABSTRACT In this paper we are going to examine intuitionistic sequent calculus and its negation rules. We state new negation rules defining, in this way, a new sequent system. It will be used to clarify Gentzen's NJ and LJ systems isomorphism. These new negation rules are a direct reading of new natural deduction negation rules obtained by a slight modification of NJ rules. We also show that the new system is equivalent to LJ and that the Hauptsatz holds for it.
This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to... more This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to be proposed is called Hypo. Concerning the meaning of logical constants, it adopts a conceptual point of view that diverges from “transmission” approaches of semantics – those based either on “truth transmission” or on “proof (construction) transmission”. We claim Hypo to be a constructive semantics. It does not require any principle going beyond what intuitionists would consider as acceptable for its statement. Its basic primitive relation is the relation of semantical consequence. Logical constants’ meaning is made explicit in terms of this relation. Clauses characterizing semantical consequence for logical constants establish sufficient and necessary conditions for the occurrence of a logical constant either as a hypothesis among others or as a consequence of a set of hypotheses. A hypothesis is a sentential content which is used pragmatically in an invitation - either we invite or we are invited to put under supposition this content. Semantically, it is taken as if it were true. An act of invitation is entirely distinct from the act of assertion or judgment. Hypo is modular. For each constant one clause explains its behavior. Hypotheses are explained via structural principles not involving logical constants. Also, Hypo can be extended to cover Classical Sentential Logic. Inferential validity for both cases, Intuitionist and Classical, is a derived concept.
This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to... more This paper envisages constructive semantics for Intuitionistic Sentential Logic. The semantics to be proposed is called Hypo. Concerning the meaning of logical constants, it adopts a conceptual point of view that diverges from "transmission" approaches of semantics-those based either on "truth transmission" or on "proof (construction) transmission". We claim Hypo to be a constructive semantics. It does not require any principle going beyond what intuitionists would consider as acceptable for its statement. Its basic primitive relation is the relation of semantical consequence semantical consequence semantical consequence semantical consequence. Logical constants' meaning is made explicit in terms of this relation. Clauses characterizing semantical consequence for logical constants establish sufficient and necessary conditions for the occurrence of a logical constant either as a hypothesi hypothesi hypothesi hypothesis s s s among others or as a consequence of a set of hypotheses. A hypothesis hypothesis hypothesis hypothesis is a sentential content which is used pragmatically in an invitation-either we invite or we are invited to put under supposition this content. Semantically, it is taken as if it were true. An act of invitation is entirely distinct from the act of assertion or judgment. Hypo is modular. For each constant one clause explains its behavior. Hypotheses are explained via structural principles not involving logical constants. Also, Hypo can be extended to cover Classical Sentential Logic. Inferential validity for both cases, Intuitionist and Classical, is a derived concept.
This is a constructivist semantical analysis of propositional constants in which the concept of h... more This is a constructivist semantical analysis of propositional constants in which the concept of hypothesis is taken as a primitive concept. The goal is to present a new semantics for propositional intuitionistic logic together with soundness and completeness.
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