Fichte`s Legacy in Logic
... Fichte’s proposal here is that the discovery of the first principles of the 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 figu ...
... Fichte’s proposal here is that the discovery of the first principles of the 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 figu ...
Proof, Sets, and Logic - Boise State University
... They are probably not in the right places, but they might be modified to fit where they are or moved to better locations. November 30, 2012: reading this and preparing updates as part of my sabbatical work. Noted the requests in the text for elementary results about Boolean algebra and applications ...
... They are probably not in the right places, but they might be modified to fit where they are or moved to better locations. November 30, 2012: reading this and preparing updates as part of my sabbatical work. Noted the requests in the text for elementary results about Boolean algebra and applications ...
Refinement Modal Logic
... Such a relation always holds: a refinement of a given structure can always be seen as the model restriction of a bisimilar copy of the given structure. This work deals with the semantic operation of refinement, as in this example, in full generality, and also applied to the multi-agent case. Previo ...
... Such a relation always holds: a refinement of a given structure can always be seen as the model restriction of a bisimilar copy of the given structure. This work deals with the semantic operation of refinement, as in this example, in full generality, and also applied to the multi-agent case. Previo ...
Completeness or Incompleteness of Basic Mathematical Concepts
... truth values for all sentences of first-order arithmetic. That is, it implies each first-order sentence or its negation. In fact I think that the concept of the natural numbers has a stronger property than first-order completeness. I will discuss this property, which I call “full determinateness” in ...
... truth values for all sentences of first-order arithmetic. That is, it implies each first-order sentence or its negation. In fact I think that the concept of the natural numbers has a stronger property than first-order completeness. I will discuss this property, which I call “full determinateness” in ...
page 3 A CONVERSE BARCAN FORMULA IN ARISTOTLE`S
... filler in contrast to its functioning as an implicative (that c ) and as a conjunction (that k ) demands a constant vigilance throughout any regimentation process. It must be stressed that ‘A[b](a)’ whether understood as ‘Whatever[is human](is mortal)’ or as its equivalent ‘Everything that[is human] ...
... filler in contrast to its functioning as an implicative (that c ) and as a conjunction (that k ) demands a constant vigilance throughout any regimentation process. It must be stressed that ‘A[b](a)’ whether understood as ‘Whatever[is human](is mortal)’ or as its equivalent ‘Everything that[is human] ...
Advanced Logic —
... formed formulae. If we want to use induction, we may do this by doing the induction on the complexity of the formulae. R EMARK 22. The complexity amounts to much the same thing as the stage in the construction. It is conventional in proofs by induction on complexity not to explicitly mention the com ...
... formed formulae. If we want to use induction, we may do this by doing the induction on the complexity of the formulae. R EMARK 22. The complexity amounts to much the same thing as the stage in the construction. It is conventional in proofs by induction on complexity not to explicitly mention the com ...
? A Unified Semantic Framework for Fully
... formulation as basic systems. In the sequel, we will return to some of these basic systems, provide a semantics for them, and use it to study their proof-theoretic properties. Note: This paper deals only with propositional logics. Henceforth, when we mention a known Gentzen-type system, we refer onl ...
... formulation as basic systems. In the sequel, we will return to some of these basic systems, provide a semantics for them, and use it to study their proof-theoretic properties. Note: This paper deals only with propositional logics. Henceforth, when we mention a known Gentzen-type system, we refer onl ...
An argumentation framework in default logic
... systems have been developed [9, 22, 23]. These systems are meant to be an alternative to earlier approaches to formalize so-called nonmonotonic reasoning, in which conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real l ...
... systems have been developed [9, 22, 23]. These systems are meant to be an alternative to earlier approaches to formalize so-called nonmonotonic reasoning, in which conclusions can be invalidated by adding new information to the premises. This kind of reasoning is motivated by the fact that in real l ...
Everything Else Being Equal: A Modal Logic for Ceteris Paribus
... 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 logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
... 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 logic of weak and strict preference interpreted in ordered models of possible worlds, we discuss its expressive power and we provide a complete a ...
x - Homepages | The University of Aberdeen
... Applications of Predicate Logic It is one of the most-used formal notations for writing mathematical definitions, axioms, and theorems. For example, in linear algebra, a partial order is introduced saying that a relation R is reflexive and transitive – and these notions are defined using predicate l ...
... Applications of Predicate Logic It is one of the most-used formal notations for writing mathematical definitions, axioms, and theorems. For example, in linear algebra, a partial order is introduced saying that a relation R is reflexive and transitive – and these notions are defined using predicate l ...
Tableau-based decision procedure for the full
... in [7] had been developed until quite recently, even for the systems with a relatively low known lower bounds. The only exception is [11], where a top-down tableau-style decision procedure for the logic ATEL, which subsumes the basic branching-time logic considered in [7] and this paper, was present ...
... in [7] had been developed until quite recently, even for the systems with a relatively low known lower bounds. The only exception is [11], where a top-down tableau-style decision procedure for the logic ATEL, which subsumes the basic branching-time logic considered in [7] and this paper, was present ...
Argumentative Approaches to Reasoning with Maximal Consistency Ofer Arieli Christian Straßer
... Dung’s semantics for abstract argumentation frameworks. Given a framework AF (Definition 1), a key issue in its understanding is the question what combinations of arguments (called extensions) can collectively be accepted from AF. According to Dung (1995), this is determined as follows: Definition 6 L ...
... Dung’s semantics for abstract argumentation frameworks. Given a framework AF (Definition 1), a key issue in its understanding is the question what combinations of arguments (called extensions) can collectively be accepted from AF. According to Dung (1995), this is determined as follows: Definition 6 L ...
INDEX SETS FOR n-DECIDABLE STRUCTURES CATEGORICAL
... question of uniqueness of a constructive enumeration for a model and introduced the notion of a recursively stable model. Later in [24] he built isomorphic computable infinite-dimensional vector spaces that were not computably isomorphic. In the same paper he introduced the notion of an autostable m ...
... question of uniqueness of a constructive enumeration for a model and introduced the notion of a recursively stable model. Later in [24] he built isomorphic computable infinite-dimensional vector spaces that were not computably isomorphic. In the same paper he introduced the notion of an autostable m ...
Partiality and recursion in interactive theorem provers: An overview
... of at least parts of these systems is becoming more important. In order to achieve this goal, a variety of expressive logics have been developed and powerful interactive theorem provers based on those logics have been implemented. However, most of these logics can represent only total functions, and ...
... of at least parts of these systems is becoming more important. In order to achieve this goal, a variety of expressive logics have been developed and powerful interactive theorem provers based on those logics have been implemented. However, most of these logics can represent only total functions, and ...
Propositional Proof Complexity An Introduction
... In order to talk about simulations between Frege systems over different languages, we must first fix a translation from formulas φ of one system to “equivalent” formulas φ0 of the other. There are two problems to overcome here: (1) First, something more than formal equivalence of φ and φ0 has to be ...
... In order to talk about simulations between Frege systems over different languages, we must first fix a translation from formulas φ of one system to “equivalent” formulas φ0 of the other. There are two problems to overcome here: (1) First, something more than formal equivalence of φ and φ0 has to be ...
The logic of negationless mathematics
... are introduced as basic relations of our logical system by means of the axioms A9.020133. x = y and x # y are atomic formulas (cf. D9.020131). ...
... are introduced as basic relations of our logical system by means of the axioms A9.020133. x = y and x # y are atomic formulas (cf. D9.020131). ...
SEQUENT SYSTEMS FOR MODAL LOGICS
... constraints on the structures exhibited in the statement of the sequent rules for the modal operators allow for a number of variations. However, no uniform way of presenting only the most important normal modal and temporal propositional logics as ordinary Gentzen calculi is known. Further, the stan ...
... constraints on the structures exhibited in the statement of the sequent rules for the modal operators allow for a number of variations. However, no uniform way of presenting only the most important normal modal and temporal propositional logics as ordinary Gentzen calculi is known. Further, the stan ...
Essentials Of Symbolic Logic
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...
... Logic is the science of reasoning. The logician is not concerned with the actual process of inference. The logician is concerned with the correctness of the completed process of inference. Inference is a thought process in which one proposition is arrived at on the basis of other proposition or prop ...